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Lithium–sulfur (Li–S) batteries are regarded as one of the most promising next-generation electrochemical cells. However, shuttling of lithium polysulfide intermediates and sluggish kinetics in random deposition of lithium sulfide (Li 2 S) have significantly degraded their capacity, rate and cycling performance. Herein, few-layered MoS 2 nanosheets enriched with sulfur vacancies are anchored inside hollow mesoporous carbon (MoS 2−x /HMC) via S–C bonding and proposed as a novel functional mediator for Li–S batteries. Ultrathin MoS 2 sheets with abundant sulfur vacancies have strong chemical affinity to polysulfides and in the meantime catalyze their fast redox conversion with enhanced reaction kinetics as proved by experimental observations and first-principles density functional theory (DFT) calculations. At a current density of 1C, the MoS 2−x /HMC-S composite cathode exhibits a high initial capacity of 945 mA h g −1 with a high retained capacity of 526 mA h g −1 and a coulombic efficiency of nearly 100% after 500 cycles. The present work sheds light on the design of novel functional electrodes for next-generation electrochemical cells based on a simple yet effective vacancy engineering strategy. 

The shuttling of polysulfides with sluggish redox kinetics has severely retarded the advancement of lithium–sulfur (Li–S) batteries. In this work oxygen-deficient titanium dioxide (TiO 2 ) has been investigated as a novel functional host for Li–S batteries. Experimental and first-principles density functional theory (DFT) studies reveal that oxygen vacancies help to reduce polysulfide shuttling and catalyze the redox kinetics of sulfur/polysulfides during cycling. Consequently, the resulting TiO 2 /S composite cathode manifests superior electrochemical properties in terms of high capacity (1472 mA h g −1 at 0.2C), outstanding rate capability (571 mA h g −1 at 2C), and excellent cycling properties (900 mA h g −1 over 100 cycles at 0.2C). The present strategy offers a viable way through vacancy engineering for the design and optimization of high-performance electrodes for advanced Li–S batteries and other electrochemical devices. 

Measurements are presented of the cross-section for the central exclusive production ofJ/\psi\to\mu^+\mu^- $J/\psi \to {\mu }^{+}{\mu }^{-}$and\psi(2S)\to\mu^+\mu^- $\psi \left(2S\right)\to {\mu }^{+}{\mu }^{-}$processes in proton-proton collisions at\sqrt{s} = 13 \ \mathrm{TeV} $\sqrt{s}=13TeV$with 2016–2018 data. They are performed by requiring both muons to be in the LHCb acceptance (with pseudorapidity2<\eta_{\mu^±} < 4.5 $2<{\eta }_{{\mu }^{\pm }}<4.5$) and mesons in the rapidity range2.0 < y < 4.5 $2.0<y<4.5$. The integrated cross-section results are\sigma_{J/\psi\to\mu^+\mu^-}(2.0 ${\sigma }_{J/\psi \to {\mu }^{+}{\mu }^{-}}(2.0<y_{J/\psi }<4.5,2.0<{\eta }_{{\mu }^{\pm }}<4.5)=400\pm 2\pm 5\pm 12pb,{\sigma }_{\psi \left(2S\right)\to {\mu }^{+}{\mu }^{-}}(2.0<y_{\psi \left(2S\right)}<4.5,2.0<{\eta }_{{\mu }^{\pm }}<4.5)=9.40\pm 0.15\pm 0.13\pm 0.27pb,$where the uncertainties are statistical, systematic and due to the luminosity determination. In addition, a measurement of the ratio of\psi(2S) $\psi \left(2S\right)$andJ/\psi $J/\psi$cross-sections, at an average photon-proton centre-of-mass energy of1\ \mathrm{TeV} $1TeV$, is performed, giving$ = 0.1763 ± 0.0029 ± 0.0008 ± 0.0039,$$ where the first uncertainty is statistical, the second systematic and the third due to the knowledge of the involved branching fractions. For the first time, the dependence of theJ/\psi$ $J/\psi$and\psi(2S) $\psi \left(2S\right)$cross-sections on the total transverse momentum transfer is determined inpp $pp$collisions and is found consistent with the behaviour observed in electron-proton collisions.