On the Modified Crystalline Stefan Problem with Singular Data

We study the behavior of solutions of the modified Stefan problem in the plane for polygonal interfaces. We are particularly interested in a solution near a singularity of either the loss of a facet or the breaking of a facet. We establish precise regularity results if a facet disappears. We use them to establish the existence of a weak solution with singular data, i.e., when some of the zero-crystalline-curvature facets have zero length.     

Analysis of Threshold Current and Wall-Plug Efficiency of Diode Lasers with Asymmetric Facet Reflectivity

Threshold current and differential quantum efficiency of broad contact lasers with asymmetric facet reflectivity are discussed with the purpose to reveal factors essential for optimisation of the wall-plug efficiency of such lasers. Lasers with low front facet reflectivity and short cavity often exhibit behaviour difficult to explain with a classical theory. More rigorous calculation performed in this work show that differential quantum efficiency is indeed less affected by a change of the front facet reflectivity or cavity length than predicted by such theory. These findings greatly simplify criteria for optimisation of the wall-plug efficiency of broad contact lasers with coated facets.     

CeO2担载Cu纳米粒子电催化CO2还原产乙烯：CeO2不同暴露晶面对催化性能的影响

Fossil fuels are expected to be the major source of energy for the next few decades. However, combustion of nonrenewable resources leads to the release of large quantities of CO₂, the primary greenhouse gas. Notably, the concentration of CO₂ in the atmosphere is increasing annually at an astounding rate. Electrochemical CO₂ reduction (ECR) to value-added fuels and chemicals using electricity from intermittent renewable energy sources is a carbon-neutral method to alleviate anthropogenic CO₂ emissions. Despite the steady progress in the selective generation of C₁ products (CO and formic acid), the production of multi-carbon species still suffers from low selectivity and efficiency. As an ECR product, ethylene (C₂H₄) has a higher energy density than do C₁ species and is an important industrial feedstock in high demand. However, the conversion of CO₂ to C₂H₄ is plagued by low productivity and large overpotential, in addition to the severe competing hydrogen evolution reaction (HER) during the ECR. To address these issues, the design and development of advanced electrocatalysts are critical. Here, we demonstrate fine-tuning of ECR to C₂H₄ by taking advantage of the prominent interaction of Cu with shape-controlled CeO₂ nanocrystals, that is, cubes, rods, and octahedra predominantly covered with (100), (110), and (111) surfaces, respectively. We found that the selectivity and activity of the ECR depended strongly on the exposed crystal facets of CeO₂. The overall ECR Faradaic efficiency (FE) over Cu/CeO₂(110) (FE ≈ 56.7%) surpassed that of both Cu/CeO₂(100) (FE ≈ 51.5%) and Cu/CeO₂(111) (FE ≈ 48.4%) in 0.1 mol·L^-1 KHCO₃ solutions with an H-type cell. This was in stark contrast to the exclusive occurrence of the HER over pure carbon paper, CeO₂(100), CeO₂(110), and CeO₂(111). In particular, the FE toward C₂H₄ formation and the partial current density increased in the sequence Cu/CeO₂(111) < Cu/CeO₂(100) < Cu/CeO₂(110) within applied bias potentials from -1.00 to -1.15 V (vs. the reversible hydrogen electrode), reaching 39.1% over Cu/CeO₂(110) at a mild overpotential (1.13 V). The corresponding values for Cu/CeO₂(100) and Cu/CeO₂(111) were FE_C2H4 ≈ 31.8% and FE_C2H4 ≈ 29.6%, respectively. The C₂H₄ selectivity was comparable to that of many reported Cu-based electrocatalysts at similar overpotentials. Furthermore, the FE for C₂H₄ remained stable even after 6 h of continuous electrolysis. The superior ECR activity of Cu/CeO₂(110) to yield C₂H₄ was attributed to the metastable (110) surface, which not only promoted the effective adsorption of CO₂ but also remarkably stabilized Cu⁺, thereby boosting the ECR to produce C₂H₄. This work offers an alternative strategy to enhance the ECR efficiency by crystal facet engineering.     

Facets for the cut cone I

We study facets of the cut coneC _n , i.e., the cone of dimension 1/2n(n – 1) generated by the cuts of the complete graph onn vertices. Actually, the study of the facets of the cut cone is equivalent in some sense to the study of the facets of the cut polytope. We present several operations on facets and, in particular, a lifting procedure for constructing facets ofC _n+1 from given facets of the lower dimensional coneC _n . After reviewing hypermetric valid inequalities, we describe the new class of cycle inequalities and prove the facet property for several subclasses. The new class of parachute facets is developed and other known facets and valid inequalities are presented.     

Strong Morphological Effect of Mn3O4 Nanocrystallites on the Catalytic Activity of Mn3O4 and Au/Mn3O4 in Benzene Combustion

Gold nanoparticles (3–4 nm) were deposited on Mn₃O₄ nanocrystallites with three distinct morphologies (cubic, hexagonal, and octahedral). The resulting structures were characterized, and their activities for benzene combustion were evaluated. The dominant exposed facets for the three kinds of Mn₃O₄ polyhedrons show the activity order: (103)≈(200)>(101). A similar activity order was derived for the interfaces between the Au and the Mn₃O₄ facet: Au/(200)≈Au/(103)>Au/(101). The metal–support interactions between the Au nanoclusters and specific facets of the Mn₃O₄ polyhedrons lead to a unique interfacial synergism in which the electronic modification of the Au nanoparticles and the morphology of the Mn₃O₄ substrate have a joint effect that is responsible for a significant enhancement in the catalytic activity of the Au/Mn₃O₄ system.     

铂修饰的{001}面暴露的二氧化钛纳米片阵列的制备和光催化性能

采用有机溶剂热法在FTO衬底上制备{001}面暴露的单晶锐钛矿相TiO2纳米片阵列,通过FESEM和XRD研究样品的形貌和晶体结构. 与水热法制备的纳米片阵列相比,有机溶剂热法制备的样品取向性更好. 采用光沉积方法在纳米片阵列上沉积Pt,所得到的Pt纳米颗粒粒径更为均匀,并且更容易沉积在{001}面上. 所负载的Pt 纳米颗粒增强了TiO2纳米片的光吸收性能,同时大大减弱了光致发光强度. 在光催化性能测试中,具有最优负载量的样品催化性能提高了一倍. 与传统的Pt负载相比,{001}面的最优负载量显得相当小,这可能源于高活性{001}面的原子结构.     

The Origin of Shape Sensitivity in Palladium‐Catalyzed Suzuki–Miyaura Cross Coupling Reactions

The shape sensitivity of Pd catalysts in Suzuki–Miyaura coupling reactions is studied using nanocrystals enclosed by well‐defined surface facets. The catalytic performance of Pd nanocrystals with cubic, cuboctahedral and octahedral morphologies are compared. Superior catalytic reactivity is observed for Pd NCs with {100} surface facets compared to {111} facets. The origin of the enhanced reactivity associated with a cubic morphology is related to the leaching susceptibility of the nanocrystals. Molecular oxygen plays a key role in facilitating the leaching of Pd atoms from the surface of the nanocrystals. The interaction of O₂ with Pd is itself facet‐dependent, which in turn gives rise to more efficient leaching from {100} facets, compared to {111} facets under the reaction conditions.     

丙烯直接环氧化Cu基催化剂的研究进展与挑战

作为一种重要的化工原料,环氧丙烷年产量近千万吨,然而目前工业上制备环氧丙烷的方法仍然面临着成本高、副产物多以及污染严重等问题。直接氧气氧化法进行丙烯环氧化因为具有原子经济、环保等优点受到了越来越多的关注。但是,催化过程中丙烯的α-H和环氧丙烷都具有很高的活性,使得在高转化率的条件下提升环氧丙烷选择性成为一个巨大的挑战。研究者们发现相较于其他币族金属,Cu基催化剂表现出更优异的丙烯直接环氧化反应性能。本综述总结梳理了近年来关于Cu基催化剂催化丙烯直接环氧化反应的研究成果,聚焦于Cu基催化剂改性方法,并对Cu基催化剂依然存在的问题和挑战进行深入探讨。     

高指数晶面纳米催化剂的电化学制备及应用

催化剂的性能与其表面结构及组成密切相关,高指数晶面纳米晶的表面含有高密度的台阶原子等活性位点而表现出较高的催化活性. 本文综述了电化学方波电位方法用于Pt、Pd、Rh等贵金属高指数晶面结构纳米晶催化剂的制备、形成机理及其电催化性能的研究. 针对贵金属利用率问题,还着重介绍了具有较高质量活性的小粒径Pt二十四面体的制备. 在此基础上,还介绍了电化学方波电位方法用于低共熔溶剂中制备高指数晶面纳米晶,以及高指数晶面纳米催化剂的表面修饰及应用;最后对高指数晶面纳米催化剂的发展做出了展望.