Single-atom Fe Embedded Co3S4 for Efficient Electrocatalytic Oxygen Evolution Reaction

Constructing atomically dispersed active sites with densely exposed and dispersed double metal-S_x catalytic sites for favorable OER catalytic activity remains rare and challenging. Herein, we design and construct a Fe₁S_x@Co₃S₄ electrocatalyst with Fe single atoms epitaxially confined in Co₃S₄ nanosheets for catalyzing the sluggish alkaline oxygen evolution reaction(OER). Consequently, in ultralow concentration alkaline solutions(0.1 mol/L KOH), such a catalyst is highly active and robust for OER with low overpotentials of 300 and 333 mV at current densities of 10 and 30 mA/cm², respectively, accompanying long-term stability without significant degradation even for 350 h. In addition, Fe₁S_x@Co₃S₄ shows a turnover frequency(TOF) value of 0.18 s⁻¹, nearly three times that of Co₃S₄(0.07 s⁻¹), suggesting the higher atomic utilization of Fe single atoms. Mössbauer and in-situ Raman spectra confirm that the OER activity of Fe₁S_x@Co₃S₄ origins from a thin catalytic layer of Co(Fe)OOH that interacts with trace-level Fe species in the electrolyte, creating dynamically stable active sites. Combined with experimental characterizations, it suggests that the most active S-coordinated dual-metal site configurations are 2S-bridged (Fe-Co)S₄, in which Co-S and Fe-S moieties are shared with two S atoms, which can strongly regulate the adsorption energy of reaction intermediates, accelerating the OER reaction kinetics.     

Information percolation and cutoff for the random‐cluster model

We consider the random‐cluster model (RCM) on with parameters p∈(0,1) and q ≥ 1. This is a generalization of the standard bond percolation (with edges open independently with probability p) which is biased by a factor q raised to the number of connected components. We study the well‐known Fortuin‐Kasteleyn (FK)‐dynamics on this model where the update at an edge depends on the global geometry of the system unlike the Glauber heat‐bath dynamics for spin systems, and prove that for all small enough p (depending on the dimension) and any q>1, the FK‐dynamics exhibits the cutoff phenomenon at with a window size , where λ_∞ is the large n limit of the spectral gap of the process. Our proof extends the information percolation framework of Lubetzky and Sly to the RCM and also relies on the arguments of Blanca and Sinclair who proved a sharp mixing time bound for the planar version. A key aspect of our proof is the analysis of the effect of a sequence of dependent (across time) Bernoulli percolations extracted from the graphical construction of the dynamics, on how information propagates.     

A solvent-governed surface state strategy for rational synthesis of N and S co-doped carbon dots with multicolour fluorescence

ABSTRACT

Multicolour emissive carbon dots (CDs) are widely investigated by virtue of their merits on fluorescent properties. Method on heteroatom doping assisted with various solvents has been proved efficient in achieving multiple-colour-emissive CDs, especially long-wavelength emission. Herein, a synthesis of multicolour-emissive CDs by controlled surface function is reported. By tuning the thermal-pyrolysis temperature and molar ratio of reactants, optimal emission of the resulted CDs gradually shifts from blue to yellow light with the assistance of different solvents. According to the emissive relationship dependent on excitation, fluorescence lifetimes, and FT-IR of these CDs, the different surface states participated with S and N elements on the surface of carbogenic core govern fluorescent colours of the CDs. In terms of the applications, blue CDs (B-CDs) exhibits high sensitivity for ion detections of Ag⁺ and Fe³⁺, which is further illustrated to have different quenching mechanisms each other because that these ions have the affinity interaction with different surface groups of the CDs. Moreover, blue and yellow CDs solutions are mixed with PVP water solution to fabricate white-light CDs/PVP film, which exhibits stable fluorescence with a CIE coordinate of (0.32, 0.33) and endows these CDs as potentially fluorescent nanomaterial in the solid state lighting field.     

Mechanism of [3+2] Cycloaddition of Alkynes to the [Mo3S4(acac)3(py)3][PF6] Cluster

A study, involving kinetic measurements on the stopped‐flow and conventional UV/Vis timescales, ESI‐MS, NMR spectroscopy and DFT calculations, has been carried out to understand the mechanism of the reaction of [Mo₃S₄(acac)₃(py)₃][PF₆] ([ 1 ]PF₆; acac=acetylacetonate, py=pyridine) with two RC?CR alkynes (R=CH₂OH (btd), COOH (adc)) in CH₃CN. Both reactions show polyphasic kinetics, but experimental and computational data indicate that alkyne activation occurs in a single kinetic step through a concerted mechanism similar to that of organic [3+2] cycloaddition reactions, in this case through the interaction with one Mo(μ‐S)₂ moiety of [ 1 ]⁺. The rate of this step is three orders of magnitude faster for adc than that for btd, and the products initially formed evolve in subsequent steps into compounds that result from substitution of py ligands or from reorganization to give species with different structures. Activation strain analysis of the [3+2] cycloaddition step reveals that the deformation of the two reactants has a small contribution to the difference in the computed activation barriers, which is mainly associated with the change in the extent of their interaction at the transition‐state structures. Subsequent frontier molecular orbital analysis shows that the carboxylic acid substituents on adc stabilize its HOMO and LUMO orbitals with respect to those on btd due to better electron‐withdrawing properties. As a result, the frontier molecular orbitals of the cluster and alkyne become closer in energy; this allows a stronger interaction.     

Asymptotic behavior toward nonlinear waves for radially symmetric solutions of the multi-dimensional Burgers equation

The present paper is concerned with the asymptotic behaviors of radially symmetric solutions for the multi-dimensional Burgers equation on the exterior domain in ${\mathbb{R}}^n,n\ge 3$, where the boundary and far field conditions are prescribed. We show that in some case where the corresponding 1-D Riemann problem for the non-viscous part admits a shock wave, the solution tends toward a linear superposition of stationary and rarefaction waves as time goes to infinity, and also show the decay rate estimates. Furthermore, we improve the results on the asymptotic stability of the stationary waves which are treated in the previous papers [2], [3]. Finally, for the case of $n=3$, we give the complete classification of the asymptotic behaviors, which includes even a linear superposition of stationary and viscous shock waves.     

Uniform stability of semilinear wave equations with arbitrary local memory effects versus frictional dampings

This paper is concerned with the mixed initial–boundary value problem for semilinear wave equations with complementary frictional dampings and memory effects. We successfully establish uniform exponential and polynomial decay rates for the solutions to this initial–boundary value problem under much weak conditions concerning memory effects. More specifically, we obtain the exponential and polynomial decay rates after removing the fundamental condition that the memory-effect region includes a part of the system boundary, while the condition is a necessity in the previous literature; moreover, for the polynomial decay rates we only assume minimal conditions on the memory kernel function g, without the usual assumption of $g^{\prime }$ controlled by g.     

Analysis of a Cahn–Hilliard–Brinkman model for tumour growth with chemotaxis

Phase field models recently gained a lot of interest in the context of tumour growth models. Typically Darcy-type flow models are coupled to Cahn–Hilliard equations. However, often Stokes or Brinkman flows are more appropriate flow models. We introduce and mathematically analyse a new Cahn–Hilliard–Brinkman model for tumour growth allowing for chemotaxis. Outflow boundary conditions are considered in order not to influence tumour growth by artificial boundary conditions. Existence of global-in-time weak solutions is shown in a very general setting.     

Gallai’s path decomposition conjecture for graphs of small maximum degree

Gallai’s path decomposition conjecture states that the edges of any connected graph on $n$ vertices can be decomposed into at most $\frac{n+1}{2}$ paths. We confirm that conjecture for all graphs with maximum degree at most five.