广西师范大学学报（自然科学版） ›› 2021, Vol. 39 ›› Issue (5): 30-43.doi: 10.16088/j.issn.1001-6600.2020112302

• 综述 • 上一篇    下一篇

CoSe2/C催化剂在电催化氧还原中的应用研究进展

赵东江*, 马松艳, 田喜强   

  1. 绥化学院 食品与制药工程学院,黑龙江 绥化 152061
  • 收稿日期:2020-11-23 修回日期:2021-01-18 出版日期:2021-09-25 发布日期:2021-10-19
  • 通讯作者: 赵东江(1965—),男,黑龙江兰西人,绥化学院教授,博士。E-mail:zhaodongjiang1965@163.com
  • 基金资助:
    黑龙江省自然科学基金联合引导项目(LH2019B034)

Applications of CoSe2/C Catalyst in Electrocatalytic Oxygen Reduction

ZHAO Dongjiang*, MA Songyan, TIAN Xiqiang   

  1. School of Food and Pharmaceutical Engineering, Suihua University, Suihua Heilongjiang 152061, China
  • Received:2020-11-23 Revised:2021-01-18 Online:2021-09-25 Published:2021-10-19

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摘要： 介绍了铂基材料作为聚合物电解质膜燃料电池阴极催化剂的优点及存在的问题,对酸性和碱性电解液中氧还原反应机理进行了分析,讨论了氧分子在催化剂表面吸附模式对氧还原反应机理的影响。探讨了CoSe2化合物晶体结构类型与特点及其与催化性能的关系,CoSe2化合物主要有立方黄铁矿型(c-CoSe2)和正交白铁矿型(o-CoSe2)2种类型,通常c-CoSe2比o-CoSe2催化活性高。综述了CoSe2/C催化剂的研究进展,着重讨论了制备方法、表面修饰、过渡金属掺杂、Co/Se物质的量之比以及碳载体等因素对CoSe2/C催化剂的氧还原催化活性、反应机理、稳定性以及耐毒化性能的影响,提出了CoSe2/C催化剂存在的问题以及发展前景。

关键词: 聚合物膜燃料电池, 非贵金属催化剂, CoSe2化合物, 氧还原反应, 催化活性

Abstract: The advantages and major problems of platinum-based materials as cathode catalyst for polymer electrolyte membrane fuel cells (PEMFCs) are briefly introduced. The mechanisms of oxygen reduction reaction in acidic and alkaline electrolytes are analyzed and the influences of the adsorption modes of oxygen molecules on the surface of catalyst for the mechanism of oxygen reduction reaction are discussed. The crystalline structures and characteristics of CoSe2 compound and the relationship with catalytic properties are discussed. The CoSe2 compound mainly consists of cubic pyrite type (c-CoSe2) and orthogonal white pyrite type (o-CoSe2). Generally, c-CoSe2 has higher catalytic activity than o-CoSe2. The research progress of the CoSe2/C catalysts is reviewed. In particular, the effects of preparation method, surface modification, transition metal doping, Co/Se ratio and carbon support on the catalytic activity, reaction mechanism, stability and toxicity resistance of CoSe2/C catalysts are reviewed. The existing problems and the development prospects of the CoSe2/C catalyst are pointed out.

Key words: polymer electrolyte membrane fuel cells, non-noble metal catalysts, CoSe2 compound, oxygen reduction reaction, catalytic activity

中图分类号: 

  • O643.36
[1] WANG X X, SOKOLOWSKI J, LIU H, et al. Pt alloy oxygen-reduction electrocatalysts: synthesis, structure, and property[J]. Chinese Journal of Catalysis, 2020, 41(5): 739-755. DOI: 10.1016/S1872-2067(19)63407-8.
[2] HYUN K, LEE J H, YOON C W, et al. The effect of platinum based bimetallic electrocatalysts on oxygen reduction reaction of proton exchange membrane fuel cells[J]. International Journal of Electrochemical Science, 2013, 8(10): 11752-11767.
[3] WU J B, YANG H. Platinum-based oxygen reduction electrocatalysts[J]. Accounts of Chemical Research, 2013, 46(8): 1848-1857. DOI:10.1021/ar300359w.
[4] HIGGINS D C, WU J, LI W M, et al. Cyanamide derived thin film on carbon nanotubes as metal free oxygen reduction reaction electrocatalyst[J]. Electrochim Acta, 2012, 59: 8-13. DOI:10.1016/j.electacta.2011.09.065.
[5] JAOUEN F, PROIETTI E, LEFEVRE M, et al. Recent advances in non-precious metal catalysis for oxygen-reduction reaction in polymer electrolyte fuel cells[J]. Energy and Environmental Science, 2011, 4(1): 114-130. DOI:10.1039/c0ee00011f.
[6] SUI S, WANG X Y, ZHOU X T, et al. A comprehensive review of Pt electrocatalysts for the oxygen reduction reaction: nanostructure, activity, mechanism and carbon support in PEM fuel cells[J]. Journal of Materials Chemistry, 2017, 5(5): 1808-1825. DOI:10.1039/c6ta08580f.
[7] 赵拓, 罗二桂, 王显, 等. 铂基氧还原催化剂在活性和稳定性方面的挑战[J]. 电化学, 2020, 26(1): 84-95. DOI:10.13208/j.electrochem.181205.
[8] 米春霞, 彭鹏, 向中华. 非碳化策略制备氧还原电催化剂[J]. 科学通报, 2020, 65(14): 1348-1357. DOI:10.1360/TB-2019-0890.
[9] ALONSO-VANTE N, TRIBUTSCH H. Energy conversion catalysis using semiconducting transition metal cluster compounds[J]. Nature, 1986, 323: 431-432.
[10] FENG Y J, GAGO A, TIMPERMAN L, et al. Chalcogenide metal centers for oxygen reduction reaction: activity and tolerance[J]. Electrochimica Acta, 2011, 56(3): 1009-1022. DOI:10.1016/j.electacta.2010.09.085.
[11] GAO M R, JIANG J, YU S H. Solution-based synthesis and design of late transition metal chalcogenide materials for oxygen reduction reaction (ORR)[J]. Small, 2012, 8(1): 13-27.DOI:10.1002/smll.201101573.
[12] SHAO M M, CHANG Q W, DODELET J P, et al. Recent advances in electrocatalysts for oxygen reduction reaction[J]. Chemical Reviews, 2016, 116(6): 3594-3657. DOI:10.1021/acs.chemrev.5b00462.
[13] DOU S, WANG X, WANG S Y. Rational design of transition metal-based materials for highly efficient electrocatalysis[J]. Small Methods, 2019, 3(1): 1800211. DOI:10.1002/smtd.201800211.
[14] BEHRET H, BINDER H, SANDSTEDE G. Electrocatalytic oxygen reduction with thiospinels and other sulphides of transition metals[J]. Electrochimica Acta, 1975, 20(2): 111-117. DOI:10.1016/0013-4686(75)90047-X.
[15] ZHU L, SUSAC D, TEO M, et al. Investigation of CoS2-based thin films as model catalysts for the oxygen reduction reaction[J]. Journal of Catalysis, 2008, 258: 235-242. DOI:10.1016/j.jcat.2008.06.016.
[16] JIRKOVSKY J S, BJORLING A, AHLBERG E. Reduction of oxygen on dispersed nanocrystalline CoS2[J]. Journal of Physical Chemistry C, 2012, 116(46): 24436-24444. DOI:10.1021/jp307669k.
[17] ZHOU Y X, YAO H B, WANG Y, et al. Hierarchical hollow Co9S8 microspheres: solvothermal synthesis, magnetic, electrochemical, and electrocatalytic properties[J]. Chemistry, 2010, 16(39): 12000-12007. DOI:10.1002/chem.200903263.
[18] ZHAO D J, MA S Y, YIN G P. A facile one-step synthesis of Co9S8 electrocatalyst for oxygen reduction reaction[J]. Rare Metal Materials and Engineering, 2017, 46(12): 3577-3582. DOI:10.1016/S1875-5372(18)30040-7.
[19] NEKOOI P, AKBARI M, AMINI M K. CoSe nanoparticles prepared by the microwave-assisted polyol method as an alcohol and formic acid tolerant oxygen reduction catalyst[J]. International Journal of Hydrogen Energy, 2010, 35(12): 6392-6398. DOI:10.1016/j.ijhydene.2010.03.134.
[20] NEKOOI P, AHMADI R, AMINI M K. Preparation of CoSe nanoparticles by microwave-assisted polyol method: effect of Se/Co ratio, support type and synthesis conditions on oxygen reduction activity[J]. Journal of the Iranian Chemical Society, 2012, 9: 715-722. DOI:10.1007/s13738-012-0077-4.
[21] FENG Y J, HE T, ALONSO-VANTE N. Oxygen reduction reaction on carbon-supported CoSe2 nanoparticles in an acidic medium[J]. Electrochimica Acta, 2009, 54(22): 5252-5256. DOI:10.1016/j.electacta.2009.03.052.
[22] FENG Y J, ALONSO-VANTE N. Carbon-supported cubic CoSe2 catalysts for oxygen reduction reaction in alkaline medium[J]. Electrochimica Acta, 2012, 72: 129-133. DOI:10.1016/j.electacta.2012.04.003.
[23] ZHU L, TEO M, WONG P C, et al. Synthesis, characterization of a CoSe2 catalyst for the oxygen reduction reaction[J]. Applied Catalyst A: General, 2010, 386(1/2): 157-165. DOI:10.1016/j.apcata.2010.07.048.
[24] YU B B, JIN J Y, WU H M, et al. Iron and nickel doped CoSe2 as efficient non precious metal catalysts for oxygen reduction[J]. International Journal of Hydrogen Energy, 2017, 42(1): 236-242. DOI:10.1016/j.ijhydene.2016.10.052.
[25] ZHAO Y, ZHANG C X, FAN R, et al. Selenium decorated reduced graphene oxide supported CoSe2 nanoparticles as efficient electrochemical catalyst for the oxygen reduction reaction[J]. Chem Electro Chem, 2018, 5(21): 3287-3292. DOI:10.1002/celc.201800796.
[26] FENG Y J, HE T, ALONSO-VANTE N. Carbon-supported CoSe2 nanoparticles for oxygen reduction reaction in acid medium[J]. Fuel Cells, 2010, 10(1): 77-83. DOI:10.1002/fuce.200900038.
[27] ZHAO D J, MA S Y. Oxygen electroreduction on CoSe2 nanoparticles prepared via hydrothermal method in acidic medium[J]. Chemical Research in Chinese Universities, 2015, 31(3): 447-451. DOI:10.1007/s40242-015-4401-2.
[28] YEAGER E. Electrocatalysts for O2 reduction[J]. Electrochimica Acta, 1984, 29(11): 1527-1537. DOI:10.1016/0013-4686(84)85006-9.
[29] YEAGER E. Dioxygen electrocatalysis: mechanisms in relation to catalyst structure[J]. Journal of Molecular Catalyst, 1986, 38(1/2): 5-25. DOI:10.1016/0304-5102(86)87045-6.
[30] HSUEH K L, CHIN D T, SRINIVASAN S. Electrode kinetics of oxygen reduction: a theoretical and experimental analysis of the rotating ring-disc electrade method[J]. Journal of Electroanalytical Chemistry and Interfacial, 1983, 153(1/2): 79-95. DOI:10.1016/S0022-0728(83)80007-2.
[31] SHI Z, ZHANG J, LIU Z S, et al. Current status of ab initio quantum chemistry study for oxygen electroreduction on fuel cell catalysts[J]. Electrochimica Acta, 2006, 51(10): 1905-1916. DOI:10.1016/j.electacta.2005.07.006.
[32] CHOI C H, KWON H C, YOOK S, et al. Hydrogen peroxide synthesis via enhanced two-electron oxygen reduction pathway on carbon-coated Pt surface[J]. Journal of Physical Chemistry C, 2014, 118(51): 30063-30070. DOI:10.1021/jp5113894.
[33] DAI C, TIAN X K, NIE Y L, et al. Successful synthesis of 3D CoSe2 hollow microspheres with high surface roughness and its excellent performance in catalytic hydrogen evolution reaction[J]. Chemical Engineering Journal, 2017, 321: 105-112. DOI:10.1016/j.cej.2017.03.068.
[34] XIAO H Q, WANG S T, WANG C, et al. Lamellar structured CoSe2 nanosheets directly arrayed on Ti plate as an efficient electrochemical catalyst for hydrogen evolution[J]. Electrochimica Acta, 2016, 217: 156-162. DOI:10.1016/j.electacta.2016.09.043.
[35] LEE C P, CHEN W F, BILLO T, et al. Beaded stream-like CoSe2 nanoneedles array for efficient hydrogen evolution electrocatalysis[J]. Journal of Materials Chemistry A, 2016,4(12): 4553-4561. DOI:10.1039/C6TA00464D.
[36] LI H M, QIAN X L, ZHU C L, et al. Template synthesis of CoSe2/Co3Se4 nanotubes: tuning of their crystal structures for photovoltaics and hydrogen evolution in alkaline medium[J]. Journal of Materials Chemistry A, 2017,5(9): 4513-4526. DOI:10.1039/C6TA10718D.
[37] CHEN P Z, XU K, TAO S, et al. Phase-transformation engineering in cobalt diselenide realizing enhanced catalytic activity for hydrogen evolution in an alkaline medium[J]. Advanced Materials, 2016, 28(34): 7527-7532. DOI:10.1002/adma.201601663.
[38] WANG X, ZHUANG L Z, JIA Y, et al. Plasma-triggered synergy of exfoliation, phase transformation, and surface engineering in cobalt diselenide for enhanced water oxidation[J]. Angewandte Chemie (International ed. in English), 2018, 57(50): 16421-16425. DOI:10.1002/anie.201810199.
[39] ZHANG X L, HU S J, ZHENG Y R, et al. Polymorphic cobalt diselenide as extremely stable electrocatalyst in acidic media via a phase-mixing strategy[J]. Nature Communications, 2019, 10(1): 5338. DOI:10.1038/s41467-019-12992-y.
[40] FENG Y J, ALONSO-VANTE N. Nonprecious metal catalysts for the molecular oxygen-reduction reaction[J]. Physica Status Solidi B, 2008, 245(9): 1792-1806. DOI:10.1002/pssb.200879537.
[41] GEWIRTH A A, THORUM M S. Electroreduction of dioxygen for fuel-cell applications: materials and challenges[J]. Inorganic Chemistry, 2010, 49(8): 3557-3566. DOI:10.1021/ic9022486.
[42] ZHANG W X, YANG Z H, LIU J W, et al. A hydrothermal synthesis of orthorhombic nanocrystalline cobalt diselenide CoSe2[J]. Materials Reserach Bulletin, 2000, 35(14/15): 2403-2408. DOI:10.1016/S0025-5408(00)00437-2.
[43] YU B, QI F, ZHENG B J, et al. One-pot synthesis of self-assembled coral-like hierarchical architecture constructed by polymorphic CoSe2 nanocrystals as superior electrocatalyst for hydrogen evolution reaction[J]. Electrochimica Acta, 2018, 277: 161-167. DOI:10.1016/j.electacta.2018.05.001.
[44] FENG Y J, HE T, ALONSO-VANTE N. In situ free-surfactant synthesis and ORR-electrochemistry of carbon-supported Co3S4 and CoSe2 nanoparticles[J]. Chemistry of Materials, 2008, 20(1): 26-28. DOI:10.1021/cm7024763.
[45] LI H Y, GAO D, CHENG X. Simple microwave preparation of high activity Se-rich CoSe2/C for oxygen reduction reaction[J]. Electrochimica Acta, 2014, 138: 232-239. DOI:10.1016/j.electacta.2014.06.065.
[46] FENG Y J, HE T, ALONSO-VANTE N. Structure phase transition and oxygen reduction activity in acidic medium of carbon-supported cobalt selenide nanoparticles[J]. ECS Transactions, 2009, 25(1): 167-173. DOI:10.1149/1.3210568.
[47] ZHAO D J, ZHANG S, YIN G P, et al. Effect of Se in Co-based selenides towards oxygen reduction electrocatalytic activity[J]. Journal of Power Sources, 2012, 206: 103-107. DOI:10.1016/j.jpowsour.2012.01.018.
[48] YU B B, WU W, JIN J, et al. Facile synthesis of Co-based selenides for oxygen reduction reaction in acidic medium[J]. International Journal of Hydrogen Energy, 2016, 41(21): 8863-8870. DOI:10.1016/j.ijhydene.2016.04.074.
[49] LEE K, ZHANG L, ZHANG J J. Ternary non-noble metal chalcogenide (W-Co-Se) as electrocatalyst for oxygen reduction reaction[J]. Electrochemistry Communications, 2007, 9: 1704-1708. DOI:10.1016/j.elecom.2007.03.025.
[50] GAO M R, XU Y F, JIANG J, et al. Water oxidation electrocatalyzed by an efficient Mn3O4/CoSe2 nanocomposite[J]. Journal of the American Chemical Society, 2012, 134(6): 2930-2933. DOI:10.1021/ja211526y.
[51] OTHMAM R, DICKS A L, ZHU Z H. Non precious metal catalysts for the PEM fuel cell cathode[J]. International Journal of Hydrogen Energy, 2012, 37: 357-372. DOI:10.1016/j.ijhydene.2011.08.095.
[52] GAO M R, YAO W T, YAO H B, et al. Synthesis of unique ultrathin lamellar mesostructured CoSe2-amine (protonated) nanobelts in a binary solution[J]. Journal of the American Chemical Society, 2009, 131(22): 7486-7487. DOI:10.1021/ja900506x.
[53] GAO M R, LIU S, JIANG J, et al. In situ controllable synthesis of magnetitenanocrystals/CoSe2 hybrid nanobelts and their enhanced catalytic performance[J]. Journal of Materials Chemistry, 2010, 20(42): 9355-9361. DOI:10.1039/C0JM01547D.
[54] GAO M R, GAO Q, JIANG J, et al. A methanol-tolerant Pt/CoSe2 nanobelt cathode catalyst for direct methanol fuel cells[J]. Angew Chem Int Ed, 2011, 50(21): 4905-4908. DOI:10.1002/ange.201007036.
[55] LI H Y, ZHANG Y, CHENG X. High catalytic activity of Ru@CoSe2/C toward oxygen reduction reaction[J]. ECS Transactions, 2015, 66(24):39-46. DOI:10.1149/06624.0039ecst.
[56] HUANG Y L, FENG C Q, WU H M, et al. Hybrids of Fe3O4/CoSe2 as efficient electrocatalysts for oxygen reduction reaction[J]. Journal of Materials Science, 2018, 53: 1123-1134. DOI:10.1007/s10853-017-1603-7.
[57] WU Z S, YANG S B, SUN Y, et al. 3D Nitrogen-doped graphene aerogel-supported Fe3O4 nanoparticles as effificient electrocatalysts for the oxygen reduction reaction[J]. Journal of the American Chemical Society, 2012, 134: 9082-9085. DOI:10.1021/ja3030565.
[58] ZHANG X F, WANG X Y, LE L J, et al. Electrochemical growth of octahedral Fe3O4 with high activity and stability toward the oxygen reduction reaction[J]. Journal of Materials Chemistry A, 2015, 3(38):19273-19276. DOI:10.1039/C5TA04450B.
[59] ZHAO D J, ZHANG S, YIN G P, et al. Tungsten doped Co-Se nanocomposites as an efficient non precious metal catalyst for oxygen reduction[J]. Electrochimica Acta, 2013, 91: 179-184. DOI:10.1016/j.electacta.2013.01.001.
[60] JIN J Y, YU B B, WU H M, et al. Synthesis and electrocatalytic activity of Co1-xMoxSe2 for oxygen reduction[J]. Journal of Alloys and Compounds, 2017, 703: 652-655. DOI:10.1016/j.jallcom.2017.01.279.
[61] SARMA S C, MISHRA V, VEMURI V, et al. Breaking the O=O bond: deciphering the role of each element in highly durable CoPd2Se2 toward oxygen reduction reaction[J]. ACS Applied Energy Materials, 2020, 3: 231-239. DOI:10.1021/acsaem.9b01400.
[62] AUER E, FREUND A, PIETSCH J, et al. Carbons as supports for industrial precious metal catalysts[J]. Applied Catalysis A: Genernal, 1998, 173(2): 259-271. DOI:10.1016/S0926-860X(98)00184-7.
[63] KIM S, PARK S J. Effect of acid/base treatment to carbon blacks on preparation of carbon-supported platinum nanoclusters[J]. Electrochimica Acta, 2007, 52(9): 3013-3021. DOI:10.1016/j.electacta.2006.09.060.
[64] 郑巧玲, 刘朝杨, 程璇, 等. 碳载体对钴硒催化剂氧还原活性的影响[J]. 厦门大学学报(自然科学版), 2015, 54(5): 730-737. DOI:10.6043/j.issn.0438-0479.2015.05.018.
[65] CHAO Y S, TSAI D S, WU A P, et al. Cobalt selenide electrocatalyst supported by nitrogen-doped carbon and its stable activity toward oxygen reduction reaction[J]. International Journal of Hydrogen Energy 2013; 38(14): 5655-5664. DOI:10.1016/j.ijhydene.2013.03.006.
[66] UNNI S M, MORA-HERNANDEZ J M, KURUNGOT S, et al. CoSe2 supported on nitrogen-doped carbon nanohorns as a methanol-tolerant cathode for air-breathing microlaminar flow fuel cells[J]. Chem Electro Chem, 2015, 2(9): 1339-1345. DOI:10.1002/celc.201500154.
[67] UNNI S M, MORA-HERNANDEZ J M, LUO Y, et al. Substrate effects on the catalytic center of CoSe2 for oxygen reduction reaction[J]. ECS Transactions, 2015, 64(36): 1-9. DOI:10.1149/06436.0001ecst.
[68] WU R B, XUE Y H, LIU B, et al. Cobalt diselenide nanoparticles embedded within porous carbon polyhedra as advanced electrocatalyst for oxygen reduction reaction[J]. Journal of Power Sources, 2016, 330: 132-139. DOI:10.1016/j.jpowsour.2016.09.001.
[69] 赵东江, 马松艳, 白晓波. 掺杂石墨烯用作阴极氧还原催化剂的研究进展[J]. 炭素技术, 2015, 34(1): 1-5. DOI:10.14078/j.cnki.1001-3741.2015.01.001.
[70] 马松艳, 田喜强, 迟彩霞, 等. CoSe2/rGO复合物的水热法合成及其氧还原催化性能[J]. 炭素技术, 2019, 38(1): 14-17,40. DOI:10.14078/j.cnki.1001-3741.2019.01.004.
[71] VERJULIO R W, SANTANDER J, MA J, et al. Selective CoSe2/C cathode catalyst for passive air-breathing alkaline anion exchange membrane μ-direct methanol fuel cell (AEM-μDMFC)[J]. International Journal of Hydrogen Energy, 2016, 41(43): 19595-19600. DOI:10.1016/j.ijhydene.2016.01.132.
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