In this paper,we propose a definition for eigenvalues of odd-order tensors based on some operators.Also,we define the Schur form and the Jordan canonical form of such tensors,and discuss commuting families of tensors....In this paper,we propose a definition for eigenvalues of odd-order tensors based on some operators.Also,we define the Schur form and the Jordan canonical form of such tensors,and discuss commuting families of tensors.Furthermore,we prove some eigenvalue ine-qualities for Hermitian tensors.Finally,we introduce characteristic polynomials of odd-order tensors.展开更多
Driven by renewable or excess electrical energy,electrochemical CO_(2)reduction reaction(eCO_(2)RR)represents a promising carbon-neutral approach to generating valuable low-carbon fuels by consuming CO_(2)and H_(2)O.C...Driven by renewable or excess electrical energy,electrochemical CO_(2)reduction reaction(eCO_(2)RR)represents a promising carbon-neutral approach to generating valuable low-carbon fuels by consuming CO_(2)and H_(2)O.C_(2+)products are one of the most economically valuable products among the reduction species of eCO_(2)RR,but there are still some challenges,such as low selectivity or low current density.In this work,we showed that a copper-based metal-azolate framework(MAF),denoted as MAF-203,exhibits the high performance of eCO_(2)RR to yield C_(2+)products with the Faradaic efficiency(C_(2+))of 52.5%and a current density of 660 mA/cm^(2)at-1.2 V vs.RHE in a flow cell device under alkaline condition.Controlled experiment,in situ infrared spectroscopy and the density functional theory(DFT)calculations showed that the electron donating effect of methyl substituents on organic ligands of the copper-based MAF could enhance the ligand field and activation of key intermediates(*CO and*CHO species),thus promoting the coupling of*CO and*CHO for yielding C_(2+)products.展开更多
电催化二氧化碳还原反应(CO_(2)RR)可以将二氧化碳转化为具有高经济价值的碳氢化合物,被认为是实现碳中和并缓解能源危机的一种有潜力的技术.铜(Cu)作为一种最有应用前景的非贵金属催化剂之一,表现出较高的催化CO_(2)RR转化为多碳产物(C...电催化二氧化碳还原反应(CO_(2)RR)可以将二氧化碳转化为具有高经济价值的碳氢化合物,被认为是实现碳中和并缓解能源危机的一种有潜力的技术.铜(Cu)作为一种最有应用前景的非贵金属催化剂之一,表现出较高的催化CO_(2)RR转化为多碳产物(C_(2+))的活性.然而,电催化CO_(2)还原成C_(2+)产物涉及一个动力学过程缓慢的C-C偶联反应,这导致C_(2+)产物的选择性较低,电流密度低,阻碍了其在工业电解槽中的实际应用.同时,CO_(2)RR产物的选择性不仅取决于热力学速率决定步骤,还取决于传质控制动力学.CO_(2)RR发生在固-气-液三相反应界面,气-液的平衡扩散可以有效抑制析氢竞争反应,进而提高CO_(2)RR的反应效率.本文设计合成了一种富晶界的Cu纳米带催化剂,并构建了气-液平衡扩散的电极结构,用于高效电催化二氧化碳还原制备乙烯(C_(2)H_(4)).以一种碱式碳酸铜(Cu_(2)CO_(3)(OH)_(2))纳米带为前驱体,在原位电化学还原条件下,前驱体中的Cu2+离子获得电子被还原为金属Cu,而释放的CO_(3)2-和OH-混合阴离子调节金属Cu的生长.生成的Cu纳米带由细小的纳米颗粒堆积而成,并暴露出大量的由Cu(111),Cu(200)和Cu(220)晶面形成的富晶界结构(GBs).同时,在CO_(2)RR测试中发现催化剂层的厚度是影响CO_(2)和电解质传质的关键因素.通过调整催化层厚度,CO_(2)和电解质可以同时到达催化剂表面,参与到CO_(2)RR中,实现了气-液平衡扩散,有效抑制了氢析出副反应.在晶界效应和气-液平衡扩散的协同作用下,优化后的电极在电流密度为700 mA cm^(-2)时,对C_(2)H_(4)和C_(2+).产物的法拉第效率分别高达67.2%和82.1%.此外,C_(2)H_(4)的部分电流密度可高达505 mA cm^(-2),高于大多数文献报道的结果.原位拉曼光谱和衰减全内反射表面增强红外吸收光谱结果表明,丰富的晶;界结构增强了CO_(2)在催化剂表面的活化,显著促进了*CO中间体的形�展开更多
As an important part of carbon neutralization,carbon dioxide electroreduction reaction(CO_(2)RR)can convert CO_(2)into high value-added chemicals and fuels to realize the recycling of carbon resources and solve the pr...As an important part of carbon neutralization,carbon dioxide electroreduction reaction(CO_(2)RR)can convert CO_(2)into high value-added chemicals and fuels to realize the recycling of carbon resources and solve the problem of environmental pollution.Therefore,exploring the element species and surface structure of the catalyst plays a central role in improving the performance of the catalyst,enhancing the CO_(2)conversion efficiency and forming C1 and C_(2+)products.Here,we summarize the recent progress in the selective regulation of CO_(2)RR reaction products by different elements.In particular,we emphasize the structure-property relationship of CO_(2)RR by the microenvironment of metal center and substrate,heteroatom doping,hydrogen bond network of metal-free polymer,and construction of heterogeneous catalytic system.At the same time,the recent advances for the identification of CO_(2)RR active sites and mechanistic studies on the process of reducing CO_(2)conversion to different products are reviewed,as well as a comprehensive review to the final products.Finally,we outline the inevitable challenges faced by CO_(2)RR and present our own recommendations aimed at contributing to CO_(2)resource utilization.展开更多
Nafion as a universal polymer ionomer was widely applied for nanocatalysts electrode preparation.However,the effect of Nafion on electrocatalytic performance was often overlooked,especially for CO_(2)electrolysis.Here...Nafion as a universal polymer ionomer was widely applied for nanocatalysts electrode preparation.However,the effect of Nafion on electrocatalytic performance was often overlooked,especially for CO_(2)electrolysis.Herein,the key roles of Nafion for CO_(2)RR were systematically studied on Cu nanoparticles(NPs)electrocatalyst.We found that Nafion modifier not only inhibit hydrogen evolution reaction(HER)by decreasing the accessibility of H_(2)O from electrolyte to Cu NPs,and increase the CO_(2)concentration at electrocatalyst interface for enhancing the CO_(2)mass transfer process,but also activate CO_(2)molecule by Lewis acid-base interaction between Nafion and CO_(2)to accelerate the formation of^(*)CO,which favor of C–C coupling for boosting C_(2)product generation.Owing to these features,the HER selectivity was suppressed from 40.6%to 16.8%on optimal Cu@Nafion electrode at-1.2 V versus reversible hydrogen electrode(RHE),and as high as 73.5%faradaic efficiencies(FEs)of C_(2)products were achieved at the same applied potential,which was 2.6 times higher than that on bare Cu electrode(~28.3%).In addition,Nafion also contributed to the long-term stability by hinder Cu NPs morphology reconstruction.Thus,this work provides insights into the impact of Nafion on electrocatalytic CO_(2)RR performance.展开更多
The use of gas diffusion electrode(GDE)based flow cell can realize industrial-scale CO_(2) reduction reactions(CO_(2)RRs).Controlling local CO_(2) and CO intermediate diffusion plays a key role in CO_(2)RR toward mult...The use of gas diffusion electrode(GDE)based flow cell can realize industrial-scale CO_(2) reduction reactions(CO_(2)RRs).Controlling local CO_(2) and CO intermediate diffusion plays a key role in CO_(2)RR toward multi-carbon(C_(2+))products.In this work,local CO_(2) and CO intermediate diffusion through the catalyst layer(CL)was investigated for improving CO_(2)RR toward C_(2+)products.The gas permeability tests and finite element simulation results indicated CL can balance the CO_(2) gas diffusion and residence time of the CO intermediate,leading to a sufficient CO concentration with a suitable CO_(2)/H_(2)O supply for high C_(2+)products.As a result,an excellent selectivity of C_(2+)products~79%at a high current density of 400 mA·cm^(-2) could be obtained on the optimal 500 nm Cu CL(Cu500).This work provides a new insight into the optimization of CO_(2)/H_(2)O supply and local CO concentration by controlling CL for C_(2+)products in CO_(2)RR flow cell.展开更多
Utilizing sunlight to convert CO_(2) into chemical fuels could address the greenhouse effect and fossil fuel crisis,Heterojunction structure catalysts with oxygen vacancy are attractive in the field of photocatalytic ...Utilizing sunlight to convert CO_(2) into chemical fuels could address the greenhouse effect and fossil fuel crisis,Heterojunction structure catalysts with oxygen vacancy are attractive in the field of photocatalytic CO_(2) conversion.Herein,a modified TiO_(2)/In_(2)O_(3)(R-P2 5/In_(2)O_(3-x)) type Ⅱ heterojunction composite with oxygen vacancies is designed for photocatalytic CO_(2) reduction,which exhibits excellent CO_(2) reduction activity,with a C_(2) selectivity of 56.66%(in terms of R_(electron)).In situ Fourier-transform infrared spectroscopy(DRIFTS) and time-resolved photoluminescence(TR-PL) spectroscopy are used to reveal the intermediate formation of the photocatalytic mechanism and photogenerated electron lifetime,respectively.The experimental characterizations reveal that the R-P25/In_(2)O_(3-x) composite shows a remarkable behavior for coupling C-C bonds.Besides,efficient charge separation contributes to the improved CO_(2) conversion performance of photocatalysts.This work introduces a type Ⅱ heterojunction composite photocatalyst,which promotes understanding the CO_(2) reduction mechanisms on heterojunction composites and is valuable for the development of photocatalysts.展开更多
文摘In this paper,we propose a definition for eigenvalues of odd-order tensors based on some operators.Also,we define the Schur form and the Jordan canonical form of such tensors,and discuss commuting families of tensors.Furthermore,we prove some eigenvalue ine-qualities for Hermitian tensors.Finally,we introduce characteristic polynomials of odd-order tensors.
基金supported by the National Key Research and Development Program of China(No.2021YFA1500401)the National Natural Science Foundation of China(Nos.21890380,21821003,22371304,223B2123)+1 种基金the Special Fund Project for Science and Technology Innovation Strategy of Guangdong Province,China(No.STKJ2023078)the Guangzhou Science and Technology Program,China(No.SL2023A04J01767).
文摘Driven by renewable or excess electrical energy,electrochemical CO_(2)reduction reaction(eCO_(2)RR)represents a promising carbon-neutral approach to generating valuable low-carbon fuels by consuming CO_(2)and H_(2)O.C_(2+)products are one of the most economically valuable products among the reduction species of eCO_(2)RR,but there are still some challenges,such as low selectivity or low current density.In this work,we showed that a copper-based metal-azolate framework(MAF),denoted as MAF-203,exhibits the high performance of eCO_(2)RR to yield C_(2+)products with the Faradaic efficiency(C_(2+))of 52.5%and a current density of 660 mA/cm^(2)at-1.2 V vs.RHE in a flow cell device under alkaline condition.Controlled experiment,in situ infrared spectroscopy and the density functional theory(DFT)calculations showed that the electron donating effect of methyl substituents on organic ligands of the copper-based MAF could enhance the ligand field and activation of key intermediates(*CO and*CHO species),thus promoting the coupling of*CO and*CHO for yielding C_(2+)products.
文摘电催化二氧化碳还原反应(CO_(2)RR)可以将二氧化碳转化为具有高经济价值的碳氢化合物,被认为是实现碳中和并缓解能源危机的一种有潜力的技术.铜(Cu)作为一种最有应用前景的非贵金属催化剂之一,表现出较高的催化CO_(2)RR转化为多碳产物(C_(2+))的活性.然而,电催化CO_(2)还原成C_(2+)产物涉及一个动力学过程缓慢的C-C偶联反应,这导致C_(2+)产物的选择性较低,电流密度低,阻碍了其在工业电解槽中的实际应用.同时,CO_(2)RR产物的选择性不仅取决于热力学速率决定步骤,还取决于传质控制动力学.CO_(2)RR发生在固-气-液三相反应界面,气-液的平衡扩散可以有效抑制析氢竞争反应,进而提高CO_(2)RR的反应效率.本文设计合成了一种富晶界的Cu纳米带催化剂,并构建了气-液平衡扩散的电极结构,用于高效电催化二氧化碳还原制备乙烯(C_(2)H_(4)).以一种碱式碳酸铜(Cu_(2)CO_(3)(OH)_(2))纳米带为前驱体,在原位电化学还原条件下,前驱体中的Cu2+离子获得电子被还原为金属Cu,而释放的CO_(3)2-和OH-混合阴离子调节金属Cu的生长.生成的Cu纳米带由细小的纳米颗粒堆积而成,并暴露出大量的由Cu(111),Cu(200)和Cu(220)晶面形成的富晶界结构(GBs).同时,在CO_(2)RR测试中发现催化剂层的厚度是影响CO_(2)和电解质传质的关键因素.通过调整催化层厚度,CO_(2)和电解质可以同时到达催化剂表面,参与到CO_(2)RR中,实现了气-液平衡扩散,有效抑制了氢析出副反应.在晶界效应和气-液平衡扩散的协同作用下,优化后的电极在电流密度为700 mA cm^(-2)时,对C_(2)H_(4)和C_(2+).产物的法拉第效率分别高达67.2%和82.1%.此外,C_(2)H_(4)的部分电流密度可高达505 mA cm^(-2),高于大多数文献报道的结果.原位拉曼光谱和衰减全内反射表面增强红外吸收光谱结果表明,丰富的晶;界结构增强了CO_(2)在催化剂表面的活化,显著促进了*CO中间体的形�
基金the National Natural Science Foundation of China(No.22171157).
文摘As an important part of carbon neutralization,carbon dioxide electroreduction reaction(CO_(2)RR)can convert CO_(2)into high value-added chemicals and fuels to realize the recycling of carbon resources and solve the problem of environmental pollution.Therefore,exploring the element species and surface structure of the catalyst plays a central role in improving the performance of the catalyst,enhancing the CO_(2)conversion efficiency and forming C1 and C_(2+)products.Here,we summarize the recent progress in the selective regulation of CO_(2)RR reaction products by different elements.In particular,we emphasize the structure-property relationship of CO_(2)RR by the microenvironment of metal center and substrate,heteroatom doping,hydrogen bond network of metal-free polymer,and construction of heterogeneous catalytic system.At the same time,the recent advances for the identification of CO_(2)RR active sites and mechanistic studies on the process of reducing CO_(2)conversion to different products are reviewed,as well as a comprehensive review to the final products.Finally,we outline the inevitable challenges faced by CO_(2)RR and present our own recommendations aimed at contributing to CO_(2)resource utilization.
基金financially supported by the Natural Science Foundation of Guangdong Province (2022A1515012359)the National Natural Science Foundation of China (21902121)+1 种基金the STU Scientific Research Foundation for Talents (NTF21020)the 2020 Li Ka Shing Foundation Cross-Disciplinary Research Grant (2020LKSFG09A)。
文摘Nafion as a universal polymer ionomer was widely applied for nanocatalysts electrode preparation.However,the effect of Nafion on electrocatalytic performance was often overlooked,especially for CO_(2)electrolysis.Herein,the key roles of Nafion for CO_(2)RR were systematically studied on Cu nanoparticles(NPs)electrocatalyst.We found that Nafion modifier not only inhibit hydrogen evolution reaction(HER)by decreasing the accessibility of H_(2)O from electrolyte to Cu NPs,and increase the CO_(2)concentration at electrocatalyst interface for enhancing the CO_(2)mass transfer process,but also activate CO_(2)molecule by Lewis acid-base interaction between Nafion and CO_(2)to accelerate the formation of^(*)CO,which favor of C–C coupling for boosting C_(2)product generation.Owing to these features,the HER selectivity was suppressed from 40.6%to 16.8%on optimal Cu@Nafion electrode at-1.2 V versus reversible hydrogen electrode(RHE),and as high as 73.5%faradaic efficiencies(FEs)of C_(2)products were achieved at the same applied potential,which was 2.6 times higher than that on bare Cu electrode(~28.3%).In addition,Nafion also contributed to the long-term stability by hinder Cu NPs morphology reconstruction.Thus,this work provides insights into the impact of Nafion on electrocatalytic CO_(2)RR performance.
基金The authors gratefully thank the National Natural Science Foundation of China(No.22002189)Central South University Research Programme of Advanced Interdisciplinary Studies(No.2023QYJC012)+1 种基金Central South University Innovation-Driven Research Program(No.2023CXQD042)the Fundamental Research Funds for the Central Universities of Central South University(No.2023ZZTS0962).
文摘The use of gas diffusion electrode(GDE)based flow cell can realize industrial-scale CO_(2) reduction reactions(CO_(2)RRs).Controlling local CO_(2) and CO intermediate diffusion plays a key role in CO_(2)RR toward multi-carbon(C_(2+))products.In this work,local CO_(2) and CO intermediate diffusion through the catalyst layer(CL)was investigated for improving CO_(2)RR toward C_(2+)products.The gas permeability tests and finite element simulation results indicated CL can balance the CO_(2) gas diffusion and residence time of the CO intermediate,leading to a sufficient CO concentration with a suitable CO_(2)/H_(2)O supply for high C_(2+)products.As a result,an excellent selectivity of C_(2+)products~79%at a high current density of 400 mA·cm^(-2) could be obtained on the optimal 500 nm Cu CL(Cu500).This work provides a new insight into the optimization of CO_(2)/H_(2)O supply and local CO concentration by controlling CL for C_(2+)products in CO_(2)RR flow cell.
基金National Research Foundation (NRF) of Korea grant funded by the Korea Government (MSIT) (NRF-2022R1A2C2093415)partially funding from the Circle Foundation (Republic of Korea) (Grant Number: 2023 TCF Innovative Science Project-03))partially Korea Basic Science Institute (National Research Facilities and Equipment Center) grant funded by the Ministry of Education (2022R1A6C101A751)。
文摘Utilizing sunlight to convert CO_(2) into chemical fuels could address the greenhouse effect and fossil fuel crisis,Heterojunction structure catalysts with oxygen vacancy are attractive in the field of photocatalytic CO_(2) conversion.Herein,a modified TiO_(2)/In_(2)O_(3)(R-P2 5/In_(2)O_(3-x)) type Ⅱ heterojunction composite with oxygen vacancies is designed for photocatalytic CO_(2) reduction,which exhibits excellent CO_(2) reduction activity,with a C_(2) selectivity of 56.66%(in terms of R_(electron)).In situ Fourier-transform infrared spectroscopy(DRIFTS) and time-resolved photoluminescence(TR-PL) spectroscopy are used to reveal the intermediate formation of the photocatalytic mechanism and photogenerated electron lifetime,respectively.The experimental characterizations reveal that the R-P25/In_(2)O_(3-x) composite shows a remarkable behavior for coupling C-C bonds.Besides,efficient charge separation contributes to the improved CO_(2) conversion performance of photocatalysts.This work introduces a type Ⅱ heterojunction composite photocatalyst,which promotes understanding the CO_(2) reduction mechanisms on heterojunction composites and is valuable for the development of photocatalysts.
