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Hydrothermally fabricated NdTe hollow shells thermally vaporized on Ni foam for water-splitting in alkaline media

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Abstract

Electrochemical water-splitting is not sparingly viable due to the slow anodic oxygen evolution reaction (OER). The need to engineer and fabricate electro-catalysts of low over-potential for water oxidation necessitates using readily available technologies and precursors. In the present study, OER electro-catalyst with composition neodymium telluride hollow shells vaporized on Ni Foam (NdTe-HS/NF) is fabricated at a substantially lower energy cost than other abundant metal-containing catalytic structures. The catalytic system functions properly, starting the oxygen evolution process at an over-potential of 301 mV vs. RHE, attaining a current density of 10 mA cm−2 and a modest Tafel slope of 91 mV dec−1 is also achieved. This tafel slope value suggests the presence of an electron/proton transfer channel. The catalyst sustains a constant current density over lengthy periods of up to 9 h of water electrolysis testing. Because of an easily accessible production technique, NdTe-HS/NF maintains its integrity, form, and chemical profile even after several hours of nonstop water electrolysis.

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The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

References

  1. Z.W. Seh, J. Kibsgaard, C.F. Dickens, I. Chorkendorff, J.K. Nørskov, T.F. Jaramillo, Combining theory and experiment in electrocatalysis: insights into materials design. Science (2017). https://doi.org/10.1126/science.aad4998

    Article  Google Scholar 

  2. Y. Liu, H. Cheng, M. Lyu, S. Fan, Q. Liu, W. Zhang, Y. Zhi, C. Wang, C. Xiao, S. Wei, Low overpotential in vacancy-rich ultrathin CoSe2 nanosheets for water oxidation. J. Am. Chem. Soc. 136, 15670–15675 (2014)

    Article  Google Scholar 

  3. D. Taherinia, M. Moazzeni, S. Moravej, Comparison of hydrothermal and electrodeposition methods for the synthesis of CoSe2/CeO2 nanocomposites as electrocatalysts toward oxygen evolution reaction. Int. J. Hydrogen Energy. 47(40), 1760–17661 (2022)

    Article  Google Scholar 

  4. L. Liang, Z. Shi, X. Tan, S. Sun, M. Chen, D. Dastan, B. Dong, L. Cao, Largely improved breakdown strength and discharge efficiency of layer-structured nanocomposites by filling with a small loading fraction of 2d zirconium phosphate nanosheets. Adv. Mater. Interfaces 9, 2101646 (2022)

    Article  Google Scholar 

  5. Ü. Ağbulut, S. Sarıdemir, A general view to converting fossil fuels to cleaner energy source by adding nanoparticles. Int. J. Ambient Energy 42, 1569–1574 (2021)

    Article  Google Scholar 

  6. S. Ullah, U. Shamraiz, A. Badshah, B. Raza, A.S. Farooqi, H.M. Tofil, M.A. Zeb, A. Alfantazi, Sulfur enriched cobalt-based layered double hydroxides for oxygen evolution reactions. Int. J. Hydrogen Energy (2021). https://doi.org/10.1016/j.ijhydene.2021.09.201

    Article  Google Scholar 

  7. M.U. Nisa, S. Manzoor, A.G. Abid, N. Tamam, M. Abdullah, M. Najam-Ul-Haq, M. Al-Buriahi, Z. Alrowaili, Z.M. Mahmoud, M.N. Ashiq, CdSe supported SnO2 nanocomposite with strongly hydrophilic surface for enhanced overall water splitting. Fuel 321, 124086 (2022)

    Article  Google Scholar 

  8. A.G. Abid, S. Manzoor, M. Usman, T. Munawar, M.U. Nisa, F. Iqbal, M.N. Ashiq, M. Najam-ul-Haq, A. Shah, M. Imran, Scalable synthesis of sm2o3/fe2o3 hierarchical oxygen vacancy-based gyroid-inspired morphology: with enhanced electrocatalytic activity for oxygen evolution performance. Energy Fuels 35, 17820–17832 (2021)

    Article  Google Scholar 

  9. P. Yin, Z. Shi, L. Sun, P. Xie, D. Dastan, K. Sun, R. Fan, Improved breakdown strengths and energy storage properties of polyimide composites: the effect of internal interfaces of C/SiO2 hybrid nanoparticles. Polym. Compos. 42, 3000–3010 (2021)

    Article  Google Scholar 

  10. M. Asadzadeh, F. Tajabadi, D. Dastan, P. Sangpour, Z. Shi, N. Taghavinia, Facile deposition of porous fluorine doped tin oxide by Dr Blade method for capacitive applications. Ceram Inter 47, 5487–5494 (2021)

    Article  Google Scholar 

  11. G. Li, F. Yin, Z. Lei, X. Zhao, X. He, Z. Li, X. Yu, Se-doped cobalt oxide nanoparticle as highly-efficient electrocatalyst for oxygen evolution reaction. Int. J. Hydrogen Energy 47, 216–227 (2022)

    Article  Google Scholar 

  12. Y. Wei, W. Li, D. Li, L. Yi, W. Hu, Amorphous-crystalline cobalt-molybdenum bimetallic phosphide heterostructured nanosheets as Janus electrocatalyst for efficient water splitting. Int. J. Hydrogen Energy 47, 7783–7792 (2022)

    Article  Google Scholar 

  13. M.Y. urRehman, S. Manzoor, N. Nazar, A.G. Abid, A.M. Qureshi, A.H. Chughtai, K.S. Joya, A. Shah, M.N. Ashiq, Facile synthesis of novel carbon dots@ metal organic framework composite for remarkable and highly sustained oxygen evolution reaction. J. Alloys. Compounds 856, 158038 (2021)

    Article  Google Scholar 

  14. M. Sadaqat, S. Manzoor, L. Nisar, A. Hassan, D. Tyagi, J.H. Shah, M.N. Ashiq, K.S. Joya, T. Alshahrani, M. Najam-ul-Haq, Iron doped nickel ditelluride hierarchical nanoflakes arrays directly grown on nickel foam as robust electrodes for oxygen evolution reaction. Electrochim. Acta 371, 137830 (2021)

    Article  Google Scholar 

  15. T. Munawar, F. Mukhtar, M.S. Nadeem, S. Manzoor, M.N. Ashiq, K. Mahmood, S. Batool, M. Hasan, F. Iqbal, Fabrication of dual Z-scheme TiO2-WO3-CeO2 heterostructured nanocomposite with enhanced photocatalysis, antibacterial, and electrochemical performance. J. Alloy. Compd. 898, 162779 (2022)

    Article  Google Scholar 

  16. Q. Yue, T. Gao, H. Yuan, D. Xiao, An efficient way to improve water splitting electrocatalysis by electrodepositing cobalt phosphide nanosheets onto copper nanowires. Int. J. Hydrog. Energy 46, 19421–19432 (2021)

    Article  Google Scholar 

  17. N. Nazar, S. Manzoor, Y. urRehman, I. Bibi, D. Tyagi, A.H. Chughtai, R.S. Gohar, M. Najam-Ul-Haq, M. Imran, M.N. Ashiq, Metal-organic framework derived CeO2/C nanorod arrays directly grown on nickel foam as a highly efficient electrocatalyst for OER. Fuel 307, 121823 (2022)

    Article  Google Scholar 

  18. K. Shan, Z.-Z. Yi, X.-T. Yin, L. Cui, D. Dastan, H. Garmestani, F.M. Alamgir, Diffusion kinetics mechanism of oxygen ion in dense diffusion barrier limiting current oxygen sensors. J. Alloy. Compd. 855, 157465 (2021)

    Article  Google Scholar 

  19. R. Wang, Y. Yang, Z. Sun, X. Lu, Ga doped Ni3S2 ultrathin nanosheet arrays supported on Ti3C2-MXene/Ni foam: An efficient and stable 3D electrocatalyst for oxygen evolution reaction. Int. J. Hydrogen Energy 47, 2958–2966 (2022)

    Article  Google Scholar 

  20. X. Zhang, B. Li, M. Lan, S. Yang, Q. Xie, J. Xiao, F. Xiao, S. Wang, Cation modulation of cobalt sulfide supported by mesopore-rich hydrangea-like carbon nanoflower for oxygen electrocatalysis. ACS Appl. Mater. Interfaces. 13, 18683–18692 (2021)

    Article  Google Scholar 

  21. X. Miao, L. Wu, Y. Lin, X. Yuan, J. Zhao, W. Yan, S. Zhou, L. Shi, The role of oxygen vacancies in water oxidation for perovskite cobalt oxide electrocatalysts: are more better? Chem. Commun. 55, 1442–1445 (2019)

    Article  Google Scholar 

  22. W. Li, Y. Niu, X. Wu, F. Wu, T. Li, W. Hu, Heterostructured CoSe2/FeSe2 nanoparticles with abundant vacancies and strong electronic coupling supported on carbon nanorods for oxygen evolution electrocatalysis. ACS Sustain Chem. Eng 8, 4658–4666 (2020)

    Article  Google Scholar 

  23. H. Xu, J. Cao, C. Shan, B. Wang, P. Xi, W. Liu, Y. Tang, MOF-derived hollow CoS decorated with CeOx nanoparticles for boosting oxygen evolution reaction electrocatalysis. Angew. Chem. 130, 8790–8794 (2018)

    Article  ADS  Google Scholar 

  24. K. Shan, F. Zhai, Z.-Z. Yi, X.-T. Yin, D. Dastan, F. Tajabadi, A. Jafari, S. Abbasi, Mixed conductivity and the conduction mechanism of the orthorhombic CaZrO3 based materials. Surf. Interfaces 23, 100905 (2021)

    Article  Google Scholar 

  25. K. Liu, C. Zhang, Y. Sun, G. Zhang, X. Shen, F. Zou, H. Zhang, Z. Wu, E.C. Wegener, C.J. Taubert, High-performance transition metal phosphide alloy catalyst for oxygen evolution reaction. ACS Nano 12, 158–167 (2018)

    Article  Google Scholar 

  26. L. Zhang, Q. Fan, K. Li, S. Zhang, X. Ma, First-row transition metal oxide oxygen evolution electrocatalysts: regulation strategies and mechanistic understandings, Sustainable. Energy Fuels 4, 5417–5432 (2020)

    Google Scholar 

  27. A. Shankar, R. Elakkiya, G. Maduraiveeran, Self-supported fabrication and electrochemical water splitting study of transition-metal sulphide nanostructured electrodes. New J. Chem. 44, 5071–5078 (2020)

    Article  Google Scholar 

  28. X. Xia, L. Wang, N. Sui, V.L. Colvin, W.Y. William, Recent progress in transition metal selenide electrocatalysts for water splitting. Nanoscale 12, 12249–12262 (2020)

    Article  Google Scholar 

  29. Y. Du, X. Ding, M. Han, M. Zhu, Morphology and composition regulation of feconi prussian blue analogues to advance in the catalytic performances of the derivative ternary transition-metal phosphides for OER. ChemCatChem 12, 4339–4345 (2020)

    Article  Google Scholar 

  30. K. Wu, F. Chu, Y. Meng, K. Edalati, Q. Gao, W. Li, H.-J. Lin, Cathodic corrosion activated Fe-based nanoglass as a highly active and stable oxygen evolution catalyst for water splitting. J. Matet. Chem A 9, 12152–12160 (2021)

    Article  Google Scholar 

  31. Y. Yu, J. Zhou, Z. Sun, Novel 2D transition-metal carbides: ultrahigh performance electrocatalysts for overall water splitting and oxygen reduction. Adv. Func. Mater. 30, 2000570 (2020)

    Article  Google Scholar 

  32. X. Peng, C. Pi, X. Zhang, S. Li, K. Huo, P.K. Chu, Recent progress of transition metal nitrides for efficient electrocatalytic water splitting, Sustainable. Energy. Fuels 3, 366–381 (2019)

    Google Scholar 

  33. Y.-X. Li, D.B. Putungan, S.-H. Lin, Two-dimensional MTe2 (M= Co, Fe, Mn, Sc, Ti) transition metal tellurides as sodium ion battery anode materials: Density functional theory calculations. Phys. Lett. A 382, 2781–2786 (2018)

    Article  ADS  Google Scholar 

  34. Y. Peng, F. Zhang, Y. Zhang, X. Luo, L. Chen, Y. Shi, ZnS modified N, S dual-doped interconnected porous carbon derived from dye sludge waste as high-efficient ORR/OER catalyst for rechargeable zinc-air battery. J. Colloid Interface Sci. 616, 659–667 (2022)

    Article  ADS  Google Scholar 

  35. G. Wu, G. Cui, D. Li, P.-K. Shen, N. Li, Carbon-supported Co1. 67Te2 nanoparticles as electrocatalysts for oxygen reduction reaction in alkaline electrolyte. J. Mater. Chem. 19, 6581–6589 (2009)

    Article  Google Scholar 

  36. L. Yang, H. Xu, H. Liu, D. Cheng, D. Cao, Active site identification and evaluation criteria of in situ grown CoTe and NiTe nanoarrays for hydrogen evolution and oxygen evolution reactions. Small Methods 3, 1900113 (2019)

    Article  Google Scholar 

  37. K. Majhi, P. Karfa, S. De, R. Madhuri, Hydrothermal Synthesis of Zinc Cobalt Telluride Nanorod towards Oxygen Evolution Reaction (OER), in IOP Conference Series Materials Science and Engineering. (IOP Publishing, Bristol, 2019), p.012076

    Google Scholar 

  38. A. Rajapriya, S. Keerthana, A. Rebekah, C. Viswanathan, N. Ponpandian, Enriched oxygen vacancy promoted heteroatoms (B, P, N, and S) doped CeO2: Challenging electrocatalysts for oxygen evolution reaction (OER) in alkaline medium. Int. J. Hydrog. Energy 46, 37281–37293 (2021)

    Article  Google Scholar 

  39. Y. Attarde, The Engineering of Charge Density Waves in Lanthanum Based Layered Tellurides Through Synthesis and Characterization (Arizona State University, Tempe, 2021)

    Google Scholar 

  40. A. Badreldin, A.E. Abusrafa, A. Abdel-Wahab, Oxygen-deficient cobalt-based oxides for electrocatalytic water splitting. Chemsuschem 14, 10–32 (2021)

    Article  Google Scholar 

  41. M. Zhang, Z. Shi, J. Zhang, K. Zhang, L. Lei, D. Dastan, B. Dong, Greatly enhanced dielectric charge storage capabilities of layered polymer composites incorporated with low loading fractions of ultrathin amorphous iron phosphate nanosheets. J. Mater. Chem. C 9, 10414–10424 (2021)

    Article  Google Scholar 

  42. M.R. Gao, J. Jiang, S.H. Yu, Solution-based synthesis and design of late transition metal chalcogenide materials for oxygen reduction reaction (ORR). Small 8, 13–27 (2012)

    Article  Google Scholar 

  43. D. Dastan, Effect of preparation methods on the properties of titania nanoparticles: solvothermal versus sol–gel. Appl. Phys. A 123, 1–13 (2017)

    Article  ADS  Google Scholar 

  44. V. Raman, D. Chinnadurai, R. Rajmohan, V.T. Chebrolu, V. Rajangam, H.-J. Kim, Transition metal chalcogenide based MnSe heterostructured with NiCo 2 O 4 as a new high performance electrode material for capacitive energy storage. New J. Chem. 43, 12630–12640 (2019)

    Article  Google Scholar 

  45. S. Dhasade, S. Han, V. Fulari, A nanostructured copper telluride thin film grown at room temperature by an electrodeposition method. J. Semicond. 33, 093002 (2012)

    Article  ADS  Google Scholar 

  46. A. Ubaldini, J. Jacimovic, N. Ubrig, E. Giannini, Chloride-driven chemical vapor transport method for crystal growth of transition metal dichalcogenides. Cryst. Growth Des. 13, 4453–4459 (2013)

    Article  Google Scholar 

  47. H. Wang, W. Wang, Y.Y. Xu, M. Asif, H. Liu, B.Y. Xia, Ball-milling synthesis of Co 2 P nanoparticles encapsulated in nitrogen doped hollow carbon rods as efficient electrocatalysts. J. Mater. Chem. A 5, 17563–17569 (2017)

    Article  Google Scholar 

  48. K. Edalati, Q. Wang, H. Eguchi, H. Razavi-Khosroshahi, H. Emami, M. Yamauchi, M. Fuji, Z. Horita, Impact of TiO2-II phase stabilized in anatase matrix by high-pressure torsion on electrocatalytic hydrogen production. Mater. Res. Lett 7, 334–339 (2019)

    Article  Google Scholar 

  49. K. Shan, Z.-Z. Yi, X.-T. Yin, D. Dastan, S. Dadkhah, B.T. Coates, H. Garmestani, Mixed conductivities of A-site deficient Y, Cr-doubly doped SrTiO3 as novel dense diffusion barrier and temperature-independent limiting current oxygen sensors. Adv. Powder Technol. 31, 4657–4664 (2020)

    Article  Google Scholar 

  50. W. Zhao, C. Zhang, F. Geng, S. Zhuo, B. Zhang, Nanoporous hollow transition metal chalcogenide nanosheets synthesized via the anion-exchange reaction of metal hydroxides with chalcogenide ions. ACS Nano 8, 10909–10919 (2014)

    Article  Google Scholar 

  51. M. Sadaqat, L. Nisar, F. Hussain, M.N. Ashiq, A. Shah, M.F. Ehsan, M. Najam-Ul-Haq, K.S. Joya, Zinc-telluride nanospheres as an efficient water oxidation electrocatalyst displaying a low overpotential for oxygen evolution. J. Mater. Chem. A 7, 26410–26420 (2019)

    Article  Google Scholar 

  52. D. Dastan, S.W. Gosavi, N.B. Chaure, Studies on electrical properties of hybrid polymeric gate dielectrics for field effect transistors (Macromolecular Symposia, Wiley Online Library, 2015), pp.81–86

    Google Scholar 

  53. D. Dastan, S. Leila Panahi, A.P. Yengntiwar, A. Banpurkar, Morphological and electrical studies of titania powder and films grown by aqueous solution method. Advanced Sci Lett 22, 950–953 (2016)

    Article  Google Scholar 

  54. X. Gao, H. Zhang, Q. Li, X. Yu, Z. Hong, X. Zhang, C. Liang, Z. Lin, Hierarchical NiCo2O4 hollow microcuboids as bifunctional electrocatalysts for overall water-splitting. Angew. Chem. Int. Ed. 55, 6290–6294 (2016)

    Article  Google Scholar 

  55. S. Anantharaj, P. Karthik, S. Kundu, Petal-like hierarchical array of ultrathin Ni (OH) 2 nanosheets decorated with Ni (OH) 2 nanoburls: a highly efficient OER electrocatalyst, Catalysis. Sci. Technol 7, 882–893 (2017)

    Google Scholar 

  56. G. Ou, P. Fan, H. Zhang, K. Huang, C. Yang, W. Yu, H. Wei, M. Zhong, H. Wu, Y. Li, Large-scale hierarchical oxide nanostructures for high-performance electrocatalytic water splitting. Nano Energy 35, 207–214 (2017)

    Article  Google Scholar 

  57. M.-H. Sun, S.-Z. Huang, L.-H. Chen, Y. Li, X.-Y. Yang, Z.-Y. Yuan, B.-L. Su, Applications of hierarchically structured porous materials from energy storage and conversion, catalysis, photocatalysis, adsorption, separation, and sensing to biomedicine. Chem. Soc. Rev. 45, 3479–3563 (2016)

    Article  Google Scholar 

  58. S.H. Bae, J.E. Kim, H. Randriamahazaka, S.Y. Moon, J.Y. Park, I.K. Oh, Seamlessly conductive 3D nanoarchitecture of core–shell Ni-Co nanowire network for highly efficient oxygen evolution. Adv. Energy Mater. 7, 1601492 (2017)

    Article  Google Scholar 

  59. L. Nisar, M. Sadaqat, A. Hassan, A. Shah, M. Najam-Ul-Haq, M.N. Ashiq, M.F. Ehsan, K.S. Joya, Ultrathin CoTe nanoflakes electrode demonstrating low overpotential for overall water splitting. Fuel 280, 118666 (2020)

    Article  Google Scholar 

  60. P. Ilanchezhiyan, C. Siva, H. Cho, S. Tamilselvan, S. Seal, T. Kang, D. Kim, Aid of cobalt ions in boosting the electrocatalytic oxygen and hydrogen evolution functions of NdFeO3 perovskite nanostructures. J. Market. Res. 11, 2246–2254 (2021)

    Google Scholar 

  61. T. Lim, S. Ju, Thermochemical hydrogen generation of indium oxide thin films. AIP Adv. 7, 035207 (2017)

    Article  ADS  Google Scholar 

  62. Q. Gao, C.Q. Huang, Y.M. Ju, M.R. Gao, J.W. Liu, D. An, C.H. Cui, Y.R. Zheng, W.X. Li, S.H. Yu, Phase-selective syntheses of cobalt telluride nanofleeces for efficient oxygen evolution catalysts. Angew. Chem. Int. Ed. 56, 7769–7773 (2017)

    Article  Google Scholar 

  63. Y. Li, F. Li, X. Meng, S. Li, J. Zeng, Y. Chen, Ultrathin Co3O4 nanomeshes for the oxygen evolution reaction. ACS Catal 8(3), 1913–1920 (2018)

    Article  Google Scholar 

  64. J. Zhao, X. Li, G. Cui, X. Sun, Highly-active oxygen evolution electrocatalyzed by an Fe-doped NiCr 2 O 4 nanoparticle film. Chem. Commun. 54, 5462–5465 (2018)

    Article  Google Scholar 

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Acknowledgements

The authors express their gratitude to Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2022R26), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

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Authors and Affiliations

  1. Department of Chemistry, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh, 11671, Saudi Arabia

    Khadijah Mohammedsaleh Katubi & Muhammad Naeem Ashiq

  2. Institute of Chemical Sciences, Bahauddin Zakariya University, Multan, 60800, Pakistan

    Mehar Un Nisa, Sumaira Manzoor & Abdul Ghafoor Abid

  3. Department of Chemistry, University of Engineering and Technology, Lahore, Pakistan

    Zahoor Ahmad

  4. Department of Chemistry, Government College University, Lahore, Pakistan

    Muhammad Abdullah

  5. Department of Physics, Sakarya University, Sakarya, Turkey

    Mohammed Sultan Al-Buriahi

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  1. Khadijah Mohammedsaleh Katubi
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Katubi, K.M., Nisa, M.U., Manzoor, S. et al. Hydrothermally fabricated NdTe hollow shells thermally vaporized on Ni foam for water-splitting in alkaline media. Appl. Phys. A 128, 882 (2022). https://doi.org/10.1007/s00339-022-05988-x

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