As an effective means to improve charge carrier separation efficiency and directional transport,the gradient doping of foreign elements to build multi-homojunction structures inside catalysts has received wide attenti...As an effective means to improve charge carrier separation efficiency and directional transport,the gradient doping of foreign elements to build multi-homojunction structures inside catalysts has received wide attentions.Herein,we reported a simple and robust method to construct multi-homojunctions in black TiO_(2) nanotubes by the gradient doping of Ni species through the diffusion of deposited Ni element on the top of black TiO2 nanotubes driven by a high temperature annealing process.The gradient Ni distribution created parts of different Fermi energy levels and energy band structures within the same black TiO_(2) nanotube,which subsequently formed two series of multi-homojunctions within it.This special multi-homojunction structure largely enhanced the charge carrier separation and transportation,while the low concentration of defect states near the surface layer further inhibited carrier recombination and facilitated the surface reaction.Thus,the B-TNT-2Ni sample with the optimized Ni doping concentration exhibited an enhanced hydrogen evolution rate of~1.84 mmol·g^(−1)·h^(−1)under visible light irradiation without the assistance of noble-metal cocatalysts,~four times higher than that of the pristine black TiO_(2)nanotube array.With the capability to create multi-homojunction structures,this approach could be readily applied to various dopant systems and catalyst materials for a broad range of technical applications.展开更多
In this paper,we discuss the multi-scale homogenization theory for the second order elliptic problems with small periodic coefficients of the form xi(aij(xε) uεx(jx)) = f(x).Assuming n = 2 and u0 ∈ W 1,∞(Ω),we pr...In this paper,we discuss the multi-scale homogenization theory for the second order elliptic problems with small periodic coefficients of the form xi(aij(xε) uεx(jx)) = f(x).Assuming n = 2 and u0 ∈ W 1,∞(Ω),we present an error estimate between the homogenization solution u0(x) and the exact solution uε(x) on the Sobolev space L∞(Ω).展开更多
基金support is gratefully acknowledged from the National Natural Science Foundation of China(NSFC)(Nos.62004137,21878257,and 21978196)the Natural Science Foundation(NSF)of Shanxi Province(No.20210302123102)+4 种基金the Key Research and Development Program of Shanxi Province(No.201803D421079)the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi(No.2019L0156)the Research Project Supported by Shanxi Scholarship Council of China(No.2020-050)the Fundamental Research Funds for the Central Universities(No.2682021CX116)Sichuan Science and Technology Program(No.2020YJ0259).
文摘As an effective means to improve charge carrier separation efficiency and directional transport,the gradient doping of foreign elements to build multi-homojunction structures inside catalysts has received wide attentions.Herein,we reported a simple and robust method to construct multi-homojunctions in black TiO_(2) nanotubes by the gradient doping of Ni species through the diffusion of deposited Ni element on the top of black TiO2 nanotubes driven by a high temperature annealing process.The gradient Ni distribution created parts of different Fermi energy levels and energy band structures within the same black TiO_(2) nanotube,which subsequently formed two series of multi-homojunctions within it.This special multi-homojunction structure largely enhanced the charge carrier separation and transportation,while the low concentration of defect states near the surface layer further inhibited carrier recombination and facilitated the surface reaction.Thus,the B-TNT-2Ni sample with the optimized Ni doping concentration exhibited an enhanced hydrogen evolution rate of~1.84 mmol·g^(−1)·h^(−1)under visible light irradiation without the assistance of noble-metal cocatalysts,~four times higher than that of the pristine black TiO_(2)nanotube array.With the capability to create multi-homojunction structures,this approach could be readily applied to various dopant systems and catalyst materials for a broad range of technical applications.
基金supported by National Natural Science Foundation of China (Grant Nos.60971121,10590353,90916027,10725210)Major State Basic Research Development Program of China (973Program) (Grant No.2010CB832702)+1 种基金the State Key Laboratory of Science and Engineering Computing,Natural Science Foundation of Zhejiang Province,China (Grant No.Y6090108)Postdoctoral Science Foundation of China (Grant No.20090451454)
文摘In this paper,we discuss the multi-scale homogenization theory for the second order elliptic problems with small periodic coefficients of the form xi(aij(xε) uεx(jx)) = f(x).Assuming n = 2 and u0 ∈ W 1,∞(Ω),we present an error estimate between the homogenization solution u0(x) and the exact solution uε(x) on the Sobolev space L∞(Ω).
