Complete Phase Diagram Research Articles

Accelerated Prediction of Phase Behavior for Block Copolymer Libraries Using a Molecularly Informed Field Theory.

Solution formulations involving polymers are the basis for a wide range of products spanning consumer care, therapeutics, lubricants, adhesives, and coatings. These multicomponent systems typically show rich self-assembly and phase behavior that are sensitive to even small changes in chemistry and composition. Longstanding computational efforts have sought techniques for predictive modeling of formulation structure and thermodynamics without experimental guidance, but the challenges of addressing the long time scales and large length scales of self-assembly while maintaining chemical specificity have thwarted the emergence of general approaches. As a consequence, current formulation design remains largely Edisonian. Here, we present a multiscale modeling approach that accurately predicts, without any experimental input, the complete temperature-concentration phase diagram of model diblock polymers in solution, as established postprediction through small-angle X-ray scattering. The methodology employs a strategy whereby atomistic molecular dynamics simulations is used to parametrize coarse-grained field-theoretic models; simulations of the latter then easily surmount long equilibration time scales and enable rigorous determination of solution structures and phase behavior. This systematic and predictive approach, accelerated by access to well-defined block copolymers, has the potential to expedite in silico screening of novel formulations to significantly reduce trial-and-error experimental design and to guide selection of components and compositions across a vast range of applications.

Realizing multiorbital Hubbard model with commensurate fillings in the paramagnetic phase of triangular magnets (X = Mn, Co, Ni)

The multiorbital Hubbard model is renowned for its rich phase diagram, characterized by various filling-dependent Mott transitions. However, controlling electron filling to explore the complete phase diagram within a single material remains challenging. In this study, we investigate three members of a correlated magnet family: Na2BaX(PO4)2 (where X = Mn, Co, Ni). Our focus is on revealing their unusual electronic structure related to the different electron fillings. Despite differences in their effective angular momentum, our first-principles calculations reveal a strikingly similar flat-band electronic structure across all three systems. Remarkably, we found that their distinct valence configurations lead to a similar response to electronic correlations in the high-temperature paramagnetic phases, which nicely realizes Mott states with different electron concentrations. Thus, these systems can be conceptualized as multiorbital Hubbard models with differing electron fillings. Our work unifies the understanding of these structurally similar systems and opens new avenues for exploring correlated electronic structures with distinct fillings.

The phase diagram of Mercedes Benz model of water using nested sampling algorithm and molecular dynamics simulations

The Mercedes Benz (MB) model of water is quite popular for explaining the properties of water, but the complete phase diagram has not yet been published. In the MB model, water molecules are modelled as two-dimensional Lennard-Jones discs, with three orientation-dependent hydrogen-bonding arms arranged as in the MB logo. Nested Sampling (NS) is a powerful sampling algorithm for the parameter space that directly calculates the partition function. NS can be used for sampling the equilibrium thermodynamics of atomistic systems and allows access to all thermodynamic quantities in absolute terms, including absolute free energies and absolute entropies. Here, NS is used to calculate the phase diagram of the simple two-dimensional Mercedes-Benz (MB) model of water. 32 water particles were used in NS. While this number of particles provides sufficient agreement with the simulations, the results from fewer particles slowly begin to diverge from the result from NS with 32 particles as some of the equilibrium lines begin to shift. By combining the results from NS and molecular dynamics (MD) simulations, different phases were located and identified. In total, 5 different solid phases, 3 liquid phases and one gaseous phase were observed.

Droplet impact outcomes: Effect of wettability and Weber number

In this study, we experimentally explored the impact outcomes of droplets under a wide range of Weber numbers (0.2 ≤ We ≤ 200) and contact angles (91° ≤ θ ≤ 162°). Five impact outcomes were identified: deposition, rebound, partial rebound, receding breakup, and prompt splash. Compared to the literature, we gathered more comprehensive data on the impact outcomes at various contact angles, which were then organized into a complete phase diagram. Furthermore, we corroborated the accuracy of these outcomes through comparisons with other studies. We conducted a comprehensive analysis of the associated phenomena and underlying mechanisms of these outcomes. By introducing the concept of surface hysteresis energy, we also proposed identification criteria for partial rebound. This innovative approach provides an important reference for further understanding of droplet impact behavior and provides guidance for future research in this field.

Hidden orders and phase transitions for the fully packed quantum loop model on the triangular lattice

Quantum loop and dimer models are prototypical correlated systems with local constraints, which are not only intimately connected to lattice gauge theories and topological orders but are also widely applicable to the broad research areas of quantum materials and quantum simulation. Employing our sweeping cluster quantum Monte Carlo algorithm, we reveal the complete phase diagram of the triangular-lattice fully packed quantum loop model. Apart from the known lattice nematic (LN) solid and the even Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathbb{Z}}}_{2}$$\\end{document} quantum spin liquid (QSL) phases, we discover a hidden vison plaquette (VP) phase, which had been overlooked and misinterpreted as a QSL for more than a decade. Moreover, the VP-to-QSL continuous transition belongs to the (2 + 1)D cubic* universality class, which offers a lattice realization of the (fractionalized) cubic fixed point that had long been considered as irrelevant towards the O(3) symmetry until corrected recently by conformal bootstrap calculations. Our results are therefore of relevance to recent developments in both experiments and theory, and facilitate further investigations of hidden phases and transitions.

Higgs branch RG flows via decay and fission

Magnetic quivers have been an instrumental technique for advancing our understanding of Higgs branches of supersymmetric theories with eight supercharges. In this work, we present the “decay and fission” algorithm for unitary magnetic quivers. It enables the derivation of the complete phase (Hasse) diagram and is characterized by the following key attributes: First and foremost, the algorithm is inherently simple, just relying on convex linear algebra. Second, any magnetic quiver can only undergo decay or fission processes; these reflect the possible Higgs branch RG flows (Higgsings), and the quivers thereby generated are the magnetic quivers of the new RG fixed points. Third, the geometry of the decay or fission transition (i.e., the transverse slice) is simply read off. As a consequence, the algorithm does not rely on a complete list of minimal transitions, but rather outputs the transverse slice geometry automatically. As a proof of concept, its efficacy is showcased across various scenarios, encompassing superconformal field theories from dimensions 3 to 6, instanton moduli spaces, and little string theories. Published by the American Physical Society 2024

Probe into a novel surfactant-free microemulsion system of ethylene glycol monobutyl ether + water + diesel for crude oil removal and recovery from oily sludge

A novel surfactant-free microemulsion (SFME) system was proposed in this study, and applied in the crude oil removal and recovery from oily sludge (OS). Based on an investigation of the SFME phase behavior and solution properties, a complete ternary phase diagram was constructed. The SFME with three-liquid phase equilibrium (Winsor III type) was selected for the treatment of OS to achieve simultaneous efficient removal (up to 95.1 %) and recovery (up to 83.2 %) of crude oil. The SFME could be reused continuously for OS treatment without purification. The removal efficiency could still keep >75.9 % after 5 times of reuse, showing high reusability. The detached crude oil could be automatically recovered based on the phase equilibrium principle without additional separation. In the washing experiments, single-factor and multi-factor orthogonal tests were applied to investigate the effects of different experimental conditions on oil removal efficiency and determine the optimal experimental scheme. The treated OS was sufficiently decontaminated according to the morphology, composition, and properties analysis by scanning electron microscopy, Fourier transform infrared spectroscopy, thermogravimetric analysis and contact angle. The composition of the recovered crude oil was identical to that of commercial crude oil according to gas chromatography–mass spectrometry analysis, showing a high recovery value. The kinetic analysis revealed that crude oil desorption experienced three main stages: membrane diffusion, intra-particle diffusion and surface desorption, and identified the chemisorption was the main interaction between the oil–soil. Finally, the mechanism of SFME action was assessed for dissolution and activation based on ultra-low IFT.

On the Problem of the Distillation Separation of Secondary Alloys of Magnesium with Zinc and Magnesium with Cadmium

An alternative to the existing method of processing secondary magnesium raw materials by remelting in a salt furnace can be distillation separation into volatile metals (Mg, Zn and Cd), low-volatile metals (Al, Mn and Zr) and rare earth elements. The separation of metals may be tracked based on phase diagrams where the field boundaries of the vapor–liquid equilibrium are plotted. Due to the fact that Mg, Zn and Cd have comparable saturated vapor pressures, the possibility of the distillation separation of Mg–Zn and Mg–Cd systems using full state diagrams including the melt–vapor phase transition boundaries were determined in this work. The boundaries of these systems were calculated based on the partial values of saturated vapor, determined by the boiling point method, and presented in the form of temperature–concentration dependencies with the indicated boundaries. The field boundaries were calculated (L + V) at atmospheric pressure (101.33 kPa) and in vacuum (1.33 kPa and 0.7 kPa,) supposing the implementation of the process. The possibility of the separate extraction of zinc and cadmium from magnesium was considered using complete phase diagrams including the boundaries of the melt–steam phase transition. When considering the boundaries of the vapor–liquid equilibrium in the binary systems Mg–Zn and Mg–Cd, it was established that it is impossible to separate metals in one “evaporation–condensation” cycle in a vacuum of 1.33 and 0.7 kPa. The problem is caused by the small size of the fields (L + V) at the temperature, which suggests processes of the re-evaporation of the condensate from the previous distillation stage. The separation of zinc and cadmium from liquid alloys with magnesium under equilibrium conditions requires several repetitions of the condensate distillation process. In non-equilibrium conditions, the real processes will require a larger number of conversions. This implies the expediency of the joint evaporation of magnesium with zinc and cadmium and the use of condensate for additional charging to liquid magnesium, and the remainder of the distillation, where volatile metals such as Al, Mn, Zr and rare earth elements will be concentrated, should be directed to the preparation of ligatures for special magnesium-based alloys.

Decay and Fission of Magnetic Quivers.

In exploring supersymmetric theories with eight supercharges, the Higgs branches present an intriguing window into strong coupling dynamics. Magnetic quivers serve as crucial tools for understanding these branches. Here, we introduce the decay and fission algorithm for unitary magnetic quivers. It efficiently derives complete phase diagrams (Hasse diagrams) through convex linear algebra. It allows magnetic quivers to undergo decay or fission, reflecting Higgs branch RG flows in the theory. Importantly, the algorithm generates magnetic quivers for the RG fixed points and simplifies the understanding of transverse slice geometry with no need for a list of minimal transitions. In contrast, the algorithm hints to the existence of a new minimal transition, whose geometry and physics need to be explored.

A simple model of the soil freezing characteristic curve for saline soils with two freezing stages

Soil freezing characteristic curve (SFCC) describes the relationship between unfrozen water and subzero temperature, which is of significance for the simulation of heat, water, salt migration in cold regions. There are two phase transition stages in some saline soils, which is often explained by the phase equilibrium of bulk solution. However, the second phase transition and chemical characteristic of solute are ignored in the current coupling numerical models for freezing-thawing soils. The newest SFCC methods considering abovementioned two items are not applicable to numerical models due to complex calculation or irregularly changeable parameters. To solve those problems, a simple model was proposed in this paper. Firstly, the complete phase diagram of pore solution at icing stage was speculated from published experimental SFCCs of saline soils. Then, the temperatures of saline soils at freezing and eutectic points were quantitative expressed with phase diagram of bulk solution and SFCC of nonsaline soil, and the criteria determining whether single icing stage or icing-eutectic stage occurs in saline soils was proposed. A synthetic index was used to describe the effects of soil matrix and initial solute concentration on the exponent. Only three constant parameters were introduced to reflect the soil matrix effect on phase transition points of pore solution and the influence of chemical characteristic of solute on pore water freezing process. Finally, the model was validated by the experimental data of saline soils and showed good results and ease of use compared to a widely used theorical model for saline soil with single freezing stage and other two models both considering two phase transitions. The work provides a deeper view of freezing process in saline soils and promote the improvement of numerical simulation effect for heat, water and salt migration in seasonal freezing-thawing areas.

Study on the Phase Behavior Simulation Method of High-Salinity Reservoirs.

The presence of salinity affects the accuracy of existing correlations used in the equation of state. Moreover, the variation of salinity is often ignored in the systematic analysis of the phase diagram, resulting in a large error in the final calculation result. It is obvious that the conventional phase equilibrium calculation is not applicable in a high-salinity reservoir. By introducing the hydrocarbon-brine binary interaction coefficient and α-function, combined with the definition of salinity, and considering the variation of salinity under different pressure and temperature conditions, a more perfect phase equilibrium calculation model was established. The complete phase diagram was drawn, and the calculation results of salinity distribution are obtained. The effect of the mole percentage of water and salt content on the phase behavior was simulated. Finally, the phase distribution simulation is carried out based on the measured data. The phase state and salinity variation law of a high-salinity reservoir are obtained. According to the fluid composition of different periods, the real phase state of the high-salinity reservoir can be monitored in real time. It can provide a theoretical basis for the gas reservoir development and the dynamic evaluation of gas storage injection and production with a hydrocarbon-brine two-phase system.

Non-Markovian dynamics of open quantum systems via auxiliary particles with exact operator constraint

We introduce an auxiliary-particle field theory to treat the non-Markovian dynamics of driven-dissipative quantum systems of the Jaynes-Cummings type. It assigns an individual quantum field to each reservoir state and provides an analytic, faithful representation of the coupled system-bath dynamics. We apply the method to a driven-dissipative photon Bose-Einstein condensate (BEC) coupled to a reservoir of dye molecules with electronic and vibronic excitations. The complete phase diagram of this system exhibits a hidden, non-Hermitian phase transition separating temporally oscillating from biexponentially decaying photon density correlations within the BEC. On one hand, this provides a qualitative distinction of the thermal photon BEC from a laser. On the other hand, it shows that one may continuously tune from the BEC to the lasing phase by circumventing a critical point. This auxiliary-particle method is generally applicable to the dynamics of open, non-Markovian quantum systems. Published by the American Physical Society 2024

Role of isotropic and anisotropic Dzyaloshinskii–Moriya interaction on skyrmions, merons and antiskyrmions in the C nv symmetric system

The lattice Hamiltonian with the presence of a chiral magnetic isotropic Dzyaloshinskii–Moriya interaction (DMI) in a square and hexagonal lattice is numerically solved to give the full phase diagram consisting of skyrmions and merons in different parameter planes. The phase diagram provides the actual regions of analytically unresolved asymmetric skyrmions and merons, and it is found that these regions are substantially larger than those of symmetric skyrmions and merons. With magnetic field, a change from meron or spin spiral (SS) to skyrmion is seen. The complete phase diagram for the C nv symmetric system with anisotropic DMI is drawn and it is shown that this DMI helps to change the SS propagation direction. Finally, the well-defined region of a thermodynamically stable antiskyrmion phase in the C nv symmetric system is shown.

Phase Diagram of the Ashkin–Teller Model

The Ashkin–Teller model is a pair of interacting Ising models and has two parameters: J is a coupling constant in the Ising models and U describes the strength of the interaction between them. In the ferromagnetic case J,U>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J,U>0$$\\end{document} on the square lattice, we establish a complete phase diagram conjectured in physics in 1970s (by Kadanoff and Wegner, Wu and Lin, Baxter and others): when J<U\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J<U$$\\end{document}, the transitions for the Ising spins and their products occur at two distinct curves that are dual to each other; when J≥U\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J\\ge U$$\\end{document}, both transitions occur at the self-dual curve. All transitions are shown to be sharp using the OSSS inequality. We use a finite-size criterion argument and continuity to extend the result of Glazman and Peled (Electron J Probab 28:1-53, 2023) from a self-dual point to its neighborhood. Our proofs go through the random-cluster representation of the Ashkin–Teller model introduced by Chayes–Machta and Pfister–Velenik and we rely on couplings to FK-percolation.

Eleven competing phases in the Heisenberg-Gamma ( JΓ ) ladder

The spin-orbit generated Γ interaction is known to induce strong frustration and to be significant in realistic models of materials. To gain an understanding of the possible phases that can arise from this interaction, it is of considerable interest to focus on a limited part of parameter space in a quasi one-dimensional model where high precision numerical results can be obtained. Here we study the Heisenberg–Gamma ( JΓ ) ladder, determining the complete zero temperature phase diagram by analyzing the entanglement spectrum (ES) and energy susceptibility. A total of 11 different phases can be identified, among them the well known rung-singlet (RS) phase and 5 other phases, FM, FM-Z, FM-XY, AF and AF-Z, with conventional long-range magnetic order. The 3 ferromagnetic phases, FM, FM-Z and FM-XY simultaneously have non-zero scalar chirality. Two other phases, the antiferromagnetic Gamma (AΓ) and ferromagnetic Gamma (FΓ) phases, have previously been observed in the Kitaev–Gamma ladder, demonstrating that the AΓ-phase is a symmetry protected topological phase (SPT) protected by TR ×Rb symmetry, the product of time-reversal (TR) and π rotation around the b-axis ( Rb ), while the FΓ-phase is related to the RS phase through a local unitary transformation. The 3 remaining phases, ϒ, Ω and δ show no conventional order, a doubling of the ES and for the ϒ and Ω-phases a gap is clearly present. The δ-phase has a significantly smaller gap and displays incommensurate correlations, with a peak in the static structure factor, S(k) continuously shifting from k/π=2/3 to k=π . In the Ω-phase we find pronounced edge-states consistent with a SPT phase protected by the same TR ×Rb symmetry as the AΓ-phase. The precise nature of the ϒ and δ-phases is less clear.

Application of metric space method in quantum information in quasi-periodic systems

Due to the rapid advancement of quantum information theory, some concepts such as fidelity and entanglement entropy have been introduced into the study of quantum phase transitions, which can be used not only to identify novel matter phases but also to detect the critical point and describe the critical behavior of the quantum phase transitions. From the point of view of the metric space, these physical quantities can be understood as the distance between the two functions in the metric space. In this work, we study a class of quasi-periodic system represented by the generalized Aubry-André-Harper (AAH) model, by using the distance between various wavefunctions or density distribution functions in real space. The generalized AAH model, an ideal platform to understand Anderson localization and other novel quantum phenomena, provides rich phase diagrams including extended, localized, even critical (multifractal) phases and can be realized in a variety of experimental platforms. In the standard AAH model, we find that the extended and localized phases can be identified. In addition, there exists a one-to-one correspondence between two distinct distances. We are able to precisely identify the critical point and compute the critical exponent by fitting the numerical results of different system sizes. In the off-diagonal AAH model, a complete phase diagram including extended phase, localized phase, and critical phase is obtained and the distance of critical phases is intermediate between the localized phase and extended phase. Meanwhile, we apply the metric space method to the wave packet propagation and discover that depending on the phase, the distance between wave functions or density functions exhibits varying dynamical evolution behavior, which is characterized by the exponent of the power-law relationship varying with time. Finally, the distance between the state density distribution functions is proposed, and it effectively identifies distinct matter phases and critical points. The critical phase which displays a multifractal structure, when compared with the other two phases, has the large state density distribution function distance. In a word, by defining the distances of a function under different parameters, we provide not only a physical quantity to identify familiar phase transitions but also an intuitive way to identify different matter phases of unknown systems, phase transition points, and their critical behaviors.

Exploring the phase diagrams of multidimensional Kuramoto models

The multidimensional Kuramoto model describes the synchronization dynamics of particles moving on the surface of D-dimensional spheres, generalizing the original model where they are characterized by a single phase. Particles are represented by D-dimensional unit vectors and the coupling constant can be extended to a coupling matrix acting on the vectors. The system has a large number of independent parameters, given by the characteristic widths of the distributions of natural frequencies and the D2 entries of the coupling matrix. Moreover, as the coupling matrix breaks the rotational symmetry, the average values of the natural frequencies also play a key role in the dynamics. General phase diagrams, indicating regions in parameter space where the system exhibits different behaviors, are hard to derive analytically. Here we obtain the complete phase diagram for D=2, for arbitrary coupling matrices and Lorentzian distributions of natural frequencies. We show that the system exhibits four different phases: disordered and static synchrony (as in the original Kuramoto model), rotation of the synchronized cluster (similar to the Kuramoto-Sakaguchi model with frustration) and active synchrony, a new phase where the module of the order parameter oscillates as it rotates on the sphere. We also explore the diagrams numerically for higher dimensions, D=3 and D=4, for particular choices of coupling matrices and frequency distributions. We find that the system always exhibits the same four phases, but their location in the space of parameters depends strongly on the dimension D being even or odd, on the coupling matrix and on the shape of the distribution of natural frequencies.

Complete topological phase diagram and realization of minimum Weyl nodes in a sheared chiral crystal of elemental tellurium

Complete topological phase diagram and realization of minimum Weyl nodes in a sheared chiral crystal of elemental tellurium

Mechanism of PVDF Membrane Formation by NIPS Revisited: Effect of Precipitation Bath Nature and Polymer-Solvent Affinity.

A new interpretation of the mechanism of the polyvinylidene fluoride (PVDF) membrane formation using the nonsolvent-induced phase separation (NIPS) method based on an analysis of the complete experimental phase diagram for the three-component mixture PVDF-dimethyl acetamide (DMAc)-water is proposed. The effects of the precipitation bath's harshness and thermodynamic affinity of the polymer's solvent on the morphology, crystalline structure, transport and physical-mechanical properties of the membranes are investigated. These characteristics were studied via scanning electron microscopy, wide-angle X-ray scattering, liquid-liquid porosimetry and standard methods of physico-mechanical analysis. It is established that an increase in DMAc concentration in the precipitation bath results in the growth of mean pore size from ~60 to ~150 nm and an increase in permeance from ~2.8 to ~8 L m-2 h-1 bar-1. It was observed that pore size transformations are accompanied by changes in the tensile strength of membranes from ~9 to ~11 and to 6 MPa, which were explained by the degeneration of finger-like pores and appearance of spherulitic structures in the samples. The addition of water to the dope solution decreased both the transport (mean pore size changed from ~55 to ~25 nm and permeance reduced from ~2.8 to ~0.5 L m-2 h-1 bar-1) and mechanical properties of the membranes (tensile strength decreased from ~9 to ~6 MPa). It is possible to conclude that the best membrane quality may be reached using pure DMAc as a solvent and a precipitation bath containing 10-30% wt. of DMAc, in addition to water.

Understanding the Pathway Switch of the Oxygen Reduction Reaction from Single- to Double-/Triple-Atom Catalysts: A Dual Channel for Electron Acceptance-Backdonation.

Recently, a lot of attention has been dedicated to double- or triple-atom catalysts (DACs/TACs) as promising alternatives to platinum-based catalysts for the oxygen reduction reaction (ORR) in fuel cell applications. However, the ORR activity of DACs/TACs is usually theoretically understood or predicted using the single-site association pathway (O2 → OOH* → O* → OH* → H2O) proposed from Pt-based alloy and single-atom catalysts (SACs). Here, we investigate the ORR process on a series of graphene-supported Fe-Co DACs/TACs by means of first-principles calculation and an electrode microkinetic model. We propose that a dual channel for electron acceptance-backdonation on adjacent metal sites of DACs/TACs efficiently promotes O-O bond breakage compared with SACs, which makes ORR switch to proceed through dual-site dissociation pathways (O2 → O* + OH* → 2OH* → OH* → H2O) from the traditional single-site association pathway. Following this revised ORR network, a complete reaction phase diagram of DACs/TACs is established, where the preferential ORR pathways and activity can be described by a three-dimensional volcano plot spanned by the adsorption free energies of ΔG(O*) and ΔG(OH*). Besides, the kinetics preferability of dual-site dissociation pathways is also appropriate for other graphene- or oxide-supported DACs/TACs. The contribution of dual-site dissociation pathways, rather than the traditional single-site association pathway, makes the theoretical ORR activity of DACs/TACs in better agreement with available experiments, rationalizing the superior kinetic behavior of DACs/TACs to that of SACs. This work reveals the origin of ORR pathway switching from SACs to DACs/TACs, which broadens the ideas and lays the theoretical foundation for the rational design of DACs/TACs and may also be heuristic for other reactions catalyzed by DACs/TACs.