This survey concerns regular graphs that are extremal with respect to the number of independent sets and, more generally, graph homomorphisms. More precisely, in the family of of d-regular graphs, ...which graph G maximizes/minimizes the quantity i(G)
1/v(G)
, the number of independent sets in G normalized exponentially by the size of G? What if i(G) is replaced by some other graph parameter? We review existing techniques, highlight some exciting recent developments, and discuss open problems and conjectures for future research.
Dinitrogen reduction to ammonia using transition metal catalysts is central to both the chemical industry and the Earth's nitrogen cycle. In the Haber–Bosch process, a metallic iron catalyst and high ...temperatures (400 °C) and pressures (200 atm) are necessary to activate and cleave NN bonds, motivating the search for alternative catalysts that can transform N2 to NH3 under far milder reaction conditions. Here, the successful hydrothermal synthesis of ultrathin TiO2 nanosheets with an abundance of oxygen vacancies and intrinsic compressive strain, achieved through a facile copper‐doping strategy, is reported. These defect‐rich ultrathin anatase nanosheets exhibit remarkable and stable performance for photocatalytic reduction of N2 to NH3 in water, exhibiting photoactivity up to 700 nm. The oxygen vacancies and strain effect allow strong chemisorption and activation of molecular N2 and water, resulting in unusually high rates of NH3 evolution under visible‐light irradiation. Therefore, this study offers a promising and sustainable route for the fixation of atmospheric N2 using solar energy.
Ultrathin TiO2 nanosheets with abundant oxygen vacancies (VO) are synthesized through a facile copper‐doping strategy, exhibiting remarkable and stable performance for the photofixation of N2 to NH3 at a rate of 78.9 µmol g−1 h−1 under ambient conditions (especially up to 700 nm). The outstanding activity can be attributed to the existence of VO and compressive strain in the nanosheets.
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Photocatalytic CO2 reduction holds promise as a future technology for the manufacture of fuels and commodity chemicals. However, factors controlling product selectivity remain poorly ...understood. Herein, we compared the performance of a homologous series of Zn-based layered double hydroxide (ZnM-LDH) photocatalysts for CO2 reduction. By varying the trivalent or tetravalent metal cations in the ZnM-LDH photocatalysts (M = Ti4+, Fe3+, Co3+, Ga3+, Al3+), the product selectivity of the reaction could be precisely controlled. ZnTi-LDH afforded CH4 as the main reduction product; ZnFe-LDH and ZnCo-LDH yielded H2 exclusively from water splitting; whilst ZnGa-LDH and ZnAl-LDH generated CO. In-situ diffuse reflectance infrared measurements, valence band XPS and density function theory calculations were applied to rationalize the CO2 reduction selectivities of the different ZnM-LDH photocatalysts. The analyses revealed that the d-band center (εd) position of the M3+ or M4+ cations controlled the adsorption strength of CO2 and thus the selectivity to carbon-containing products or H2. Cations with d-band centers relatively close to the Fermi level (Ti4+, Ga3+ and Al3+) adsorbed CO2 strongly yielding CH4 or CO, whereas metal cations with d-band centers further from the Fermi level (Fe3+ and Co3+) adsorbed CO2 poorly, thereby yielding H2 only (from water splitting). Our findings clarify the role of trivalent and tetravalent metal cations in LDH photocatalysts for the selective CO2 reduction, paving new ways for the development of improved LDH photocatalyst with high selectivities to specific products.
Designing atomically dispersed metal catalysts for oxygen reduction reaction (ORR) is a promising approach to achieve efficient energy conversion. Herein, we develop a template-assisted method to ...synthesize a series of single metal atoms anchored on porous N,S-codoped carbon (NSC) matrix as highly efficient ORR catalysts to investigate the correlation between the structure and their catalytic performance. The structure analysis indicates that an identical synthesis method results in distinguished structural differences between Fe-centered single-atom catalyst (Fe-SAs/NSC) and Co-centered/Ni-centered single-atom catalysts (Co-SAs/NSC and Ni-SAs/NSC) because of the different trends of each metal ion in forming a complex with the N,S-containing precursor during the initial synthesis process. The Fe-SAs/NSC mainly consists of a well-dispersed FeN4S2 center site where S atoms form bonds with the N atoms. The S atoms in Co-SAs/NSC and Ni-SAs/NSC, on the other hand, form metal–S bonds, resulting in CoN3S1 and NiN3S1 center sites. Density functional theory (DFT) reveals that the FeN4S2 center site is more active than the CoN3S1 and NiN3S1 sites, due to the higher charge density, lower energy barriers of the intermediates, and products involved. The experimental results indicate that all three single-atom catalysts could contribute high ORR electrochemical performances, while Fe-SAs/NSC exhibits the highest of all, which is even better than commercial Pt/C. Furthermore, Fe-SAs/NSC also displays high methanol tolerance as compared to commercial Pt/C and high stability up to 5000 cycles. This work provides insights into the rational design of the definitive structure of single-atom catalysts with tunable electrocatalytic activities for efficient energy conversion.
Transformation of biomass wastes into sustainable low cost carbon materials is now a topic of great interest. Here, we describe porous carbon from biomass derived waste shrimp shells and its ...application in two different energy storage systems. The unique porous structure with the presence of heteroatoms (O, N) makes it promising material for both lithium ion batteries and supercapacitors. When applied as anode materials for lithium ion batteries, the as-prepared carbon showed a specific capacity as high as 1507 mA h g−1 and 1014 mA h g−1 at current densities of 0.1 A g−1 and 0.5 A g−1, respectively, good rate performance and superior cycling stability. The porous carbon-based supercapacitor also delivered a specific capacitance of 239 F g−1 at a current density of 0.5 A g−1 in 6 M KOH electrolyte. The specific capacitance retention is 99.4% even after 5000 charge-discharge cycles, indicating excellent cycling stability. The superior electrochemical performances for both lithium ion batteries and supercapacitors could be ascribed to the high specific surface area, porous structure and nitrogen doping effect.
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•N-doped porous carbon was synthesized from waste shrimp shells.•The material presents a high specific surface area of 1271 m2 g−1.•For Li-ion batteries, the material shows high specific capacity of 1507 mA h g−1.•For supercapacitor electrode, 99.4% capacitance retained after 5000 cycles.
Large over‐potentials owing to the sluggish kinetics of battery reactions have always been the drawbacks of Li−O2 batteries, which lead to short cycle life. Although redox mediators have been ...intensively investigated to overcome this issue, side‐reactions are generally induced by the solvated nature of redox mediators. Herein, we report an alternative method to achieve more efficient utilization of tetrathiafulvalene (TTF) in Li−O2 batteries. By coordinating TTF+ with LiCl during charging, an organic conductor TTF+Clx− precipitate covers Li2O2 to provide an additional electron‐transfer pathway on the surface, which can significantly reduce the charge over‐potential, improve the energy efficiency of Li−O2 batteries, and eliminate side‐reactions between the lithium metal anode and TTF+. When a porous graphene electrode is used, the Li−O2 battery combined with TTF and LiCl shows an outstanding performance and prolonged cycle life.
A pinch of salt: TTF+Clx− precipitates on the surface of the Li2O2 discharge product upon the addition of LiCl to tetrathiafulvalene‐containing electrolytes during charging. This efficiently reduces the risk of side‐reactions and enhances the cycling performances of Li−O2 batteries.
Semiconductor photocatalysis attracts widespread interest in water splitting, CO2 reduction, and N2 fixation. N2 reduction to NH3 is essential to the chemical industry and to the Earth's nitrogen ...cycle. Industrially, NH3 is synthesized by the Haber–Bosch process under extreme conditions (400–500 °C, 200–250 bar), stimulating research into the development of sustainable technologies for NH3 production. Herein, this study demonstrates that ultrathin layered‐double‐hydroxide (LDH) photocatalysts, in particular CuCr‐LDH nanosheets, possess remarkable photocatalytic activity for the photoreduction of N2 to NH3 in water at 25 °C under visible‐light irradiation. The excellent activity can be attributed to the severely distorted structure and compressive strain in the LDH nanosheets, which significantly enhances N2 chemisorption and thereby promotes NH3 formation.
Layered‐double‐hydroxide (LDH) nanosheets are shown to exhibit outstanding visible‐light‐driven photocatalytic activity for the reduction of N2 to NH3 under ambient conditions. Irradiation of CuCr‐LDH nanosheets in N2‐saturated water with 500 nm monochromatic light produces NH3. The excellent activity can be attributed to the severely distorted structure and compressive strain of the LDH nanosheets, promoting NH3 formation.
Nitrogen‐doped porous carbon nanosheets (N‐CNS) are synthesized by hydrothermal carbon coating of g‐C3N4 nanosheets followed by high‐temperature treatment in N2. g‐C3N4 serves as a template, nitrogen ...source, and porogen in the synthesis. This approach yields N‐CNS with a high nitrogen content and comparable oxygen reduction reaction catalytic activities to commercial Pt/C catalysts in alkaline media.
Efficient capture of solar energy will be critical to meeting the energy needs of the future. Semiconductor photocatalysis is expected to make an important contribution in this regard, delivering ...both energy carriers (especially H2) and valuable chemical feedstocks under direct sunlight. Over the past few years, carbon dots (CDs) have emerged as a promising new class of metal‐free photocatalyst, displaying semiconductor‐like photoelectric properties and showing excellent performance in a wide variety of photoelectrochemical and photocatalytic applications owing to their ease of synthesis, unique structure, adjustable composition, ease of surface functionalization, outstanding electron‐transfer efficiency and tunable light‐harvesting range (from deep UV to the near‐infrared). Here, recent advances in the rational design of CDs‐based photocatalysts are highlighted and their applications in photocatalytic environmental remediation, water splitting into hydrogen, CO2 reduction, and organic synthesis are discussed.
Carbon dots (CDs) have emerged as promising materials for various photocatalytic reactions owing to their tunable light‐harvesting range and outstanding electron‐transfer efficiency stemming from their intrinsic nanostructures. Recent advances in the rational design of CD‐based photocatalysts and their applications in photocatalytic environmental remediation, hydrogen evolution by water splitting, CO2 reduction, and organic synthesis are highlighted.
Faceted NiO nanoparticles preferentially exposing high surface energy planes demand attention due to their excellent electrocatalytic properties. However, the activity of faceted NiO nanoparticles ...generally remains suboptimal due to their large lateral size and thickness, which severely limits the availability of coordinatively unsaturated active reactive edge and corner sites. Here, ultrafine NiO nanosheets with a platelet size of ∼4.0 nm and thickness (∼1.1 nm) stabilized by TiO2 were successfully prepared by calcination of a monolayer layered double hydroxide precursor. The ultrafine NiO nanosheets displayed outstanding performance in electrochemical water oxidation due to a high proportion of reactive NiO {110} facets, intrinsic Ni3+ and Ti3+ sites, and abundant interfaces, which act synergistically to promote H2O adsorption and facilitate charge-transfer.
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