Lithium-sulfur batteries have attracted increasing attention because of their high theoretical capadty. Using sulfur/carbon composites as the cathode materials has been demonstrated as an effective strategy to optimiz...Lithium-sulfur batteries have attracted increasing attention because of their high theoretical capadty. Using sulfur/carbon composites as the cathode materials has been demonstrated as an effective strategy to optimize sulfur utilization and enhance cycle stability as well. In this work hollow-in-hollow carbon spheres with hollow foam-like cores （HCSF@C） are prepared to improve both capability and cycling stability of lithium-sulfur batteries. With high surface area and large pore volumes, the loading of sulfur in HCSF@C reaches up to 70 wt.%. In the resulting S/HCSF@C composites, the outer carbon shell serves as an effective protection layer to trap the soluble polysulfide intermediates derived from the inner component. Consequently, the S/HCSF@C cathode retains a high capacity of 780 mAh/g after 300 cycles at a high charge/discharge rate of 1 A/g.展开更多
This paper studies a class of variational problems which involving both bulk and surfaceenergies. The bulk energy is of Dirichlet type though it can be in very general forms allowingunknowns to be scalar or vectors.Th...This paper studies a class of variational problems which involving both bulk and surfaceenergies. The bulk energy is of Dirichlet type though it can be in very general forms allowingunknowns to be scalar or vectors.The surface energy is an arbitrary elliptic parametric integralwhich is defined on a free interface. One also allows other constraints such as volumes of partitioning sets. One establishes the existence and regularity theory, in particular, the regularityof the free interface of such problems.展开更多
基金We thank the National Basic Research Program of China （Nos. 2011CB932403 and 2015CB932300） and the National Natural Science Foundation of China （Nos. 21301144, 21390390, 21131005, 21333008, and 21420102001） for financial support.
文摘Lithium-sulfur batteries have attracted increasing attention because of their high theoretical capadty. Using sulfur/carbon composites as the cathode materials has been demonstrated as an effective strategy to optimize sulfur utilization and enhance cycle stability as well. In this work hollow-in-hollow carbon spheres with hollow foam-like cores （HCSF@C） are prepared to improve both capability and cycling stability of lithium-sulfur batteries. With high surface area and large pore volumes, the loading of sulfur in HCSF@C reaches up to 70 wt.%. In the resulting S/HCSF@C composites, the outer carbon shell serves as an effective protection layer to trap the soluble polysulfide intermediates derived from the inner component. Consequently, the S/HCSF@C cathode retains a high capacity of 780 mAh/g after 300 cycles at a high charge/discharge rate of 1 A/g.
文摘This paper studies a class of variational problems which involving both bulk and surfaceenergies. The bulk energy is of Dirichlet type though it can be in very general forms allowingunknowns to be scalar or vectors.The surface energy is an arbitrary elliptic parametric integralwhich is defined on a free interface. One also allows other constraints such as volumes of partitioning sets. One establishes the existence and regularity theory, in particular, the regularityof the free interface of such problems.
