Enhanced sampling of cylindrical microphase separation via a shell-averaged bond-orientational order parameter.

The formation of a hexagonal phase from disordered phase is one of the typical order-disorder transitions (ODTs) observed in asymmetric diblock copolymer systems. In order to drive this transition in a particle-based simulation, we introduce a shell-based bond-orientational order parameter that selectively responds to the mesoscopic order of the hexagonal cylinder phase. From metadynamics simulations in a bond-free particle model system, the characteristic pathway involved with the underlying free energy surface is deduced for the disordered-to-hexagonal transition. It is shown consecutively that the transition pathway and the metastable state are reproduced in dissipative particle dynamics simulations for the corresponding transition in a bulk asymmetric block copolymer melt system. These agreements suggest that efficient strategies for enhanced sampling with particle-based simulations of block copolymer systems can be devised using coarse-grained pictures of the mesoscopic order.

A corresponding-state framework for the structural transition of supercritical fluids across the Widom delta.

This work proposes a classification algorithm based on the radical Voronoi tessellation to define the Widom delta, supercritical gas-liquid coexistence region, of polyatomic molecules. Specifically, we use a weighted mean-field classification method to classify a molecule into either gaslike or liquidlike. Classical percolation theory methods are adopted to understand the generality of the structural transition and to locate the Widom delta. A structural analysis on various supercritical fluids shows that the proposed method detects the influence of the attractive interaction on the structural transition of supercritical fluids. Moreover, we demonstrate that the supercritical gas-liquid coexistence region of water overlaps with the ridges of the response function maxima. From the pressure-temperature relation, a three-parameter corresponding state theorem is derived, which states that the fraction of gaslike molecules of a substance is equal to that of another if their reduced pressure, reduced temperature, and the critical compressibility factor are the same.

Probabilistic characterization of the Widom delta in supercritical region.

We present a probabilistic classification algorithm to understand the structural transition of supercritical Lennard-Jones (LJ) fluid. The classification algorithm is designed based on the exploratory data analysis on the nearest Voronoi neighbors of subcritical vapor and liquid. The algorithm is tested and applied to LJ type fluids modeled with the truncated and shifted potential and the Weeks-Chandler-Andersen potential. The algorithm makes it available to locate the Widom delta, which encloses the supercritical gas-liquid boundary and the percolation transition loci in a geometrical manner, and to conjecture the role of attractive interactions on the structural transition of supercritical fluids. Thus, the designed algorithm offers an efficient and comprehensible method to understand the phase behavior of a supercritical mesophase.

Exploring Optimal Water Splitting Bifunctional Alloy Catalyst by Pareto Active Learning.

Design of bifunctional multimetallic alloy catalysts, which are one of the most promising candidates for water splitting, is a significant issue for the efficient production of renewable energy. Owing to large dimensions of the components and composition of multimetallic alloys, as well as the trade-off behavior in terms of the hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) overpotentials for bifunctional catalysts, it is difficult to search for high-performance bifunctional catalysts with multimetallic alloys using conventional trial-and-error experiments. Here, an optimal bifunctional catalyst for water splitting is obtained by combining Pareto active learning and experiments, where 110 experimental data points out of 77946 possible points lead to effective model development. The as-obtained bifunctional catalysts for HER and OER exhibit high performance, which is revealed by model development using Pareto active learning; among the catalysts, an optimal catalyst (Pt0.15 Pd0.30 Ru0.30 Cu0.25 ) exhibits a water splitting behavior of 1.56 V at a current density of 10 mA cm-2 . This study opens avenues for the efficient exploration of multimetallic alloys, which can be applied in multifunctional catalysts as well as in other applications.

Aligned structures of mesogenic motifs in epoxy resin and their thermal conductivities.

The epoxy-based crosslinked polymer with the mesogenic group has been studied as a candidate resin material with high thermal conductivity due to the ordered structure of the mesogenic groups. In this study, we conducted all atomic molecular dynamics simulations with iterative crosslinking procedures on various epoxy resins with mesogenic motifs to investigate the effect of molecular alignment on thermal conductivity. The stacked structure of aromatic groups in the crosslinked polymer was analyzed based on the angle-dependent radial distribution function (ARDF), where the resins were categorized into three groups depending on their monomer shapes. The thermal conductivities of resins were higher than those of conventional polymers due to the alignment of aromatic groups, but no distinct correlation with the ARDF was found. Therefore, we conducted a further study about two structural factors that affect the alignment and the TC by comparing the resins within the same groups: the monomer with an alkyl spacer and functional groups in hardeners. The alkyl chains introduced in the epoxy monomers induced more stable stacking of aromatic groups, but thermal conductivity was lowered as they inhibited phonon transfer on the microscopic scale. In the other case, the functional groups in the hardener lowered the TC when the polar interaction with other polar groups in the monomer was strong enough to compete with the pi-pi interaction. These results represent how various chemical motifs in mesogenic groups affect their alignment on the atomistic scale, and also how they have effects on the TC consequently.

Searching for an Optimal Multi-Metallic Alloy Catalyst by Active Learning Combined with Experiments.

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 Pt0.65 Ru0.30 Ni0.05 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.

Conformation Dynamics of Single Polymer Strands in Solution.

Conformational changes in macromolecules significantly affect their functions and assembly into high-level structures. Despite advances in theoretical and experimental studies, investigations into the intrinsic conformational variations and dynamic motions of single macromolecules remain challenging. Here, liquid-phase transmission electron microscopy enables the real-time tracking of single-chain polymers. Imaging linear polymers, synthetically dendronized with conjugated aromatic groups, in organic solvent confined within graphene liquid cells, directly exhibits chain-resolved conformational dynamics of individual semiflexible polymers. These experimental and theoretical analyses reveal that the dynamic conformational transitions of the single-chain polymer originate from the degree of intrachain interactions. In situ observations also show that such dynamics of the single-chain polymer are significantly affected by environmental factors, including surfaces and interfaces.

Donor-Acceptor Alternating Copolymer Compatibilizers for Thermally Stable, Mechanically Robust, and High-Performance Organic Solar Cells.

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 (PD)-SMA blends effectively reduces PD-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 PD-SMA blends. The addition of 20 wt % DACCs affords OSCs with a PCE of 17.1% and a cohesive fracture energy (Gc) of 0.89 J m-2, higher than those (PCE = 13.6% and Gc = 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.

Universality, Scaling, and Collapse in Supercritical Fluids.

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.

Phase behavior of disk-coil block copolymers under cylindrical confinement: Curvature-induced structural frustrations.

In this paper, we explore the self-assembly behavior of disk-coil block copolymers (BCPs) confined within a cylinder using molecular dynamics simulations. As functions of the diameter of the confining cylinder and the number of coil beads, concentric lamellar structures are obtained with a different number of alternating disk-rich and coil-rich bilayers. Our paper focuses on the curvature-induced structural behavior in the disk-rich domain of a self-assembled structure, which is investigated by calculating the local density distribution P(r) and the orientational distribution G(r,θ). In the inner layers of cylinder-confined disk-coil BCPs, both P(r) and G(r,θ) show characteristic asymmetry within a bilayer which is directly contrasted with the bulk and slab-confined disk-coil BCPs. We successfully explain the structural frustration of disks arising from the curved structure due to packing frustration of disks and asymmetric stretching of coils to the regions with different curvatures in a bilayer. Our results are important to understand the self-assembly behavior of BCPs containing a rigid motif in a confined structure, such as a self-assembled structure of bacteriochlorophyll molecules confined by a lipid layer to form a chlorosome, the photosynthetic antennae complex found in nature.

Topological generalization of the rigid-nonrigid transition in soft-sphere and hard-sphere fluids.

A fluid particle changes its dynamics from diffusive to oscillatory as the system density increases up to the melting density. Hence the notion of the Frenkel line was introduced to demarcate the fluid region into rigid and nonrigid liquid subregions based on the collective particle dynamics. In this work, we apply a topological framework to locate the Frenkel lines of the soft-sphere and the hard-sphere models relying on the system configurations. The topological characteristics of the ideal gas and the maximally random jammed state are first analyzed, then the classification scheme designed in our earlier work is applied to soft-sphere and hard-sphere fluids. The dependence of the classification result on the bulk density is understood based on the theory of fluid polyamorphism. The percolation behavior of solid-like clusters is described based on the fraction of solid-like molecules in an integrated manner. The crossover densities are obtained by examining the percolation of solid-like clusters. The resultant crossover densities of soft-sphere fluids converge to that of hard-sphere fluid. Hence the topological method successfully highlights the generality of the Frenkel line.

Topological extension of the isomorph theory based on the Shannon entropy.

Isomorph theory is one of the promising theories for understanding the quasiuniversal relationship between thermodynamic, dynamic, and structural characteristics. Based on the hidden scale invariance of the inverse power law potentials, it rationalizes the excess entropy scaling law of dynamic properties. This work aims to show that this basic idea of isomorph theory can be extended by examining the microstructural features of the system. Using the topological framework in conjunction with the entropy calculation algorithm, we demonstrate that Voronoi entropy, a measure of the topological diversity of single atoms, provides a scaling law for the transport properties of soft-sphere fluids, which is comparable to the frequently used excess entropy scaling. By examining the relationship between the Voronoi entropy and the solidlike fraction of simple fluids, we suggest that the Frenkel line, a rigid-nonrigid crossover line, be a topological isomorphic line at which the scaling relation qualitatively changes.

Widom Delta of Supercritical Gas-Liquid Coexistence.

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.

"Two-Phase" Thermodynamics of the Frenkel Line.

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.

Topological Characterization of Rigid-Nonrigid Transition across the Frenkel 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.