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Density and chain conformation profiles of square-well chains between two parallel walls were studied by using density-functional theory. The free energy of square-well chains is separated into two contributions: the hard-sphere repulsion and the attraction. The Heaviside function is used as the weighting function for both of the two parts. The equation of state of Hu et al. is used to calculate the excess free energy of the repulsive part. The equation of state of statistical associating fluid theory for chain molecules with attractive potentials of variable range [A. Gil-Villegas et al. J. Chem. Phys. 106, 4168 (1997)] is used to calculate the excess free energy of the attractive part. Because the wall is inaccessible to a mass center of a longer chain, there exists a sharp fall in the distribution of end-to-end distance near the wall as the chain length increases. When the average density of the system is not too low, the prediction of this work is in good agreement with computer simulation results for the density profiles and the chain conformation over a wide range of chain length, temperature, and attraction strength of the walls. However, when the average density and the temperature are very low, the prediction deviates to a certain degree from the computer simulation results for molecules with long chain length. A more accurate functional approximation is needed.

The exploration of efficient host materials of sulfur is significant for the practical lithium-sulfur (Li-S) batteries, and the hosts are expected to be highly conductive for high sulfur utilization and exhibit strong interaction toward polysulfides to suppress the shuttle effect for long-lasting cycle stability. Herein, we propose a simple synthesis of metallic cobalt-embedded N-doping carbon nanotubes (Co@NCNT) as a “two-in-one” host of sulfur for efficient Li-S batteries. In the binary host, the N-doped CNTs, cooperating with metallic Co nanoparticles, can serve as 3D conductive networks for fast electron transportation, while the synergetic effect of metallic Co and doping N heteroatoms helps to chemically confine polysulfides, acting as active sites to accelerate electrochemical kinetics. With these advantages, the S/Co@NCNT composite delivers an excellent cycling stability with a capacity decay of 0.08% per cycle averaged within 500 cycles at a current density of 1 A g–1 and a high rate performance of 530 mA h g–1 at 5 A g–1. Further, the superior electrochemical performance of the S/Co@NCNT electrode can be maintained under a high sulfur loading up to 4 mg cm–2. Our work demonstrates a feasible strategy to design promising host materials simultaneously featuring high conductivity and strong confinement toward polysulfides for high-performance Li-S batteries.

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