Skip to main content
SpringerLink
Log in

On Zagreb Type Molecular Descriptors of Ceria Oxide and Their Applications

  • Original Paper
  • Published:
Journal of Cluster Science Aims and scope Submit manuscript

Abstract

Cerium oxide is an oxide of the rare-earth metal cerium. It is a pale yellow-white powder with the chemical formula CeO2. It is an important commercial product and an intermediate in the purification of the element from the ores. Cerium oxide nanoparticles (CeO2 NPs) has gained their importance as engineered nano materials (ENMs) that have wide applications as catalysts in industry, which direct to their prominent occurrence in natural and engineered water systems. In waste water treatment plants, CeO2 NPs can stay colloidally stable and be unconstrained in the secondary effluents. As they entered into tertiary treatment , such as advanced oxidation processes (AOPs), it is noteworthy that how the generated reactive oxygen species will change the colloidal stability, aggregation, and the surface chemistry of CeO2 NPs. Chemical graph theory plays an important role in modeling and designing any chemical structure. The topological indices are the numerical invariants of a molecular graph and are very useful for predicting their physical properties. In this paper, we study the chemical graph of crystal structure of ceria oxide CeO2. Also, we compute degree based molecular descriptors(topological indices).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Sayle, T. X. T., Parker, S. C., & Catlow, C. R. A., The role of oxygen vacancies on ceria surfaces in the oxidation of carbon monoxide. Surface Science, 316.3 (1994): 329–336.

    Article  CAS  Google Scholar 

  2. Ribeiro, A. N., & Ferreira, N. D. S., Systematic study of the physical origin of ferromagnetism in \(CeO_{2^{-}} \delta\) nanoparticles. Physical Review B, 95.14, (2017): 144–150.

    Article  Google Scholar 

  3. Tseng, E. N., Hsiao, Y. T., Chen, Y. C., Chen, S. Y., Gloter, A., & Song, J. M., Magnetism and plasmonic performance of mesoscopic hollow ceria spheres decorated with silver nanoparticles. Nanoscale, 11.8, (2019): 3574–3582.

    Article  CAS  Google Scholar 

  4. Wu, X., Neil, C. W., Kim, D., Jung, H., & Jun, Y. S., Co-effects of \(UV/H_{2} O_{2}\) and natural organic matter on the surface chemistry of cerium oxide nanoparticles. Environmental Science: Nano, 5.10, (2018): 2382–2393.

    CAS  Google Scholar 

  5. Siddiqui, M. K., Imran, M., & Ahmad, A., On Zagreb indices, Zagreb polynomials of some nanostar dendrimers. Applied mathematics and computation, 280, (2016): 132–139.

    Article  Google Scholar 

  6. Shao, Z.; Siddiqui, M.K.; Muhammad, M.H.; Computing zagreb indices and zagreb polynomials for symmetrical nanotubes, Symmetry, 2018, 10 (7), 244–254.

    Article  Google Scholar 

  7. Randic, Milan. Characterization of molecular branching. Journal of the American Chemical Society, 97. 23 (1975): 6609–6615.

    Article  CAS  Google Scholar 

  8. Siddiqui, M. K., Naeem, M., Rahman, N. A., & Imran, M., Computing topological indices of certain networks. Journal of Optoelectronics and Advanced Materials, 18, (2016): 884–892.

    Google Scholar 

  9. Gao, W., Farahani, M.R., Degree-based indices computation for special chemical molecular structures using edge dividing method, Applied Mathematics and Nonlinear Sciences, 2016, 1(1), 99–122.

    Article  Google Scholar 

  10. Zali, M.R., Jamil, M. K., Imran, M., Vertex PIv Topological Index of Titania Carbon Nanotubes \(TiO2 (m, n)\), Applied Mathematics and Nonlinear Sciences, 2016, 1 (1), 170–176.

    Google Scholar 

  11. Farahani, M.R., On the Randic and Sum-Connectivity Index of Nanotubes, Applied Mathematics and Nonlinear Sciences, 2014 1 (1), 150–166.

    Google Scholar 

  12. Gutman, I.; Trinajst\(\acute{c}\), N.; Graph theory and molecular orbitals., Total \(\pi\)-electron energy of alternant hydrocarbons. Chemical Physics Letters, 1972, 17, 535–538.

  13. Gutman, I., Das, K. C., The first Zagreb index 30 years after., MATCH Commun. Math. Comput. Chem., 50, (2004): 83–92.

    CAS  Google Scholar 

  14. Do\(\check{s}\)li\(\acute{c}\), T., Vertex-weighted Wiener polynomials for composite graphs, Ars Math. Contemp  1, (2008): 66-80.

  15. Gutman, I., Furtula, B., Vukićević, Ž. K., Popivoda, G., On Zagreb Indices and Coindices, MATCH Commun. Math. Comput. Chem. 74(2015), 5–16.

    Google Scholar 

  16. Shirdel, G. H., RezaPour, H., & Sayadi, A.M., The Hyper-Zagreb Index of Graph Operations, Iranian Journal of Mathematical Chemistry, 4(2), (2013): 213–220.

    Google Scholar 

  17. Ghorbani, M., Azimi, N., Note on multiple Zagreb indices, Iranian Journal of Mathematical Chemistry, 3(2), (2012): 137–143.

    Google Scholar 

  18. Ranjini, P.S., Lokesha, V., Usha, A., Relation between phenylene and hexagonal squeez using harmonic index, Int J Graph Theory, 1, (2013): 116–121.

    Google Scholar 

  19. Gutman, I., Trinajstic, N., Graph theory and molecular orbitals total \(\varphi\)-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17, (1972):535–538.

    Article  CAS  Google Scholar 

  20. Gao, W.; Siddiqui, M. K.; Molecular Descriptors of Nanotube, Oxide, Silicate, and Triangulene networks, Journal of Chemistry, 2017, Volume 2017, Article ID 6540754, 1–10.

  21. Gao, W.; Siddiqui, M. K.; Naeem, M.; Rehman, N. A.; topological Characterization of Carbon Graphite and Crystal Cubic Carbon Structures, Molecules. 2017, 22(9), 1496–1507.

    Article  Google Scholar 

  22. Idrees, N.; Naeem, M. N.; Hussain, F.; Sadiq, A.; Siddiqui, M. K. Molecular Descriptors of Benzenoid System, Quimica Nova, 2017, 40(2), 143–145.

    CAS  Google Scholar 

  23. Nadeem, S. Ahmad, M. K. Siddiqui, M. Naeem, Topological Descriptor of 2-Dimensional Silicon Carbons and Their Applications, Open Chem. 2019; 17, 1473–1482.

    Article  CAS  Google Scholar 

  24. M. Imran , M.K. Siddiqui, A.Q. Baig, W. khalid, H.Shaker, Topological Properties of Cellular Neural Networks, Journal of Intelligent & Fuzzy Systems, 37, 2019, 3605-3614.

  25. M.K. Siddiqui, M. Imran, M. Saeed, Topological properties of face-centred cubic lattice, Hacet. J. Math. Stat. 49(1), (2020), 195–207.

    Google Scholar 

  26. Yang, H., Imran, M., Akhter, S., Iqbal, Z., Siddiqui, M. K., On Distance-Based Topological Descriptors of Subdivision Vertex-Edge Join of Three Graphs, IEEE ACCESS, 7(1), (2019), 143381–143391.

    Article  Google Scholar 

  27. Gutman, I., Das, K. C., Some Properties of the Second Zagreb Index, MATCH Commun. Math. Comput. Chem. 50(2004), 103–112.

    Google Scholar 

  28. Hu, T., Xiao, S., Yang, H., Chen, L., & Chen, Y., Cerium oxide as an efficient electron extraction layer for \(pin\) structured perovskite solar cells. Chemical communications, 54(5), (2018.): 471-474.

  29. Younis, A., D. Chu, and S. Li, Cerium oxide nanostructures and their applications in Functionalized Nanomaterials. Intech Open. 18(2016), 53–68.

    Google Scholar 

  30. Naqvi, S. T. R., Shirinfar, B., Majeed, S., Najam-ul-Haq, M., Hussain, D., Iqbal, T., & Ahmed, N., Synthesis, design and sensing applications of nanostructured ceria-based materials. Analyst, 143(23), (2018): 5610–5628.

    Article  Google Scholar 

  31. Dhall, A., W. Self, Cerium oxide nanoparticles: a brief review of their synthesis methods and biomedical applications. Antioxidants, 7(8), (2018): 97–108.

    Article  Google Scholar 

  32. Chen, K., Sun, C., Song, S., Xue, D., Polymorphic crystallization of CeO2 compound, Cryst. Eng. Comm, 16, (2014): 52–57.

    CAS  Google Scholar 

  33. Jenkins, H.D.B., Thermodynamics of the relationship between lattice energy and lattice enthalpy. Journal of chemical education, 82(6), (2005): 950–960.

    Article  CAS  Google Scholar 

  34. Bennaim, A., Discover entropy and the second law of thermodynamics: A playful way of discovering a law of nature. 2010: World Scientific.

  35. Deml, A. M., Stevanovi, V., Muhich, C. L., Musgrave, C. B., & O’Hayre, R. Oxide enthalpy of formation and band gap energy as accurate descriptors of oxygen vacancy formation energetics, Energy & Environmental Science, 7(6), (2014): 1996–2004.

    Article  CAS  Google Scholar 

Download references

Acknowledgements

The authors would like to thanks the two anonymous reviewers for their very constructive comments that helped us to enhance the quality of this manuscript.

Funding

The research was supported by the National Natural Science Foundation of China (Grant Nos. 11971142, 11871202, 61673169, 11701176, 11626101, 11601485).

Author information

Authors and Affiliations

  1. Department of Mathematics, Huzhou University, Huzhou, 313000, People’s Republic of China

    Yu-Ming Chu

  2. Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha, 410114, People’s Republic of China

    Yu-Ming Chu

  3. Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, 54000, Pakistan

    Muhammad Kamran Siddiqui & Sana Javed

  4. Department of Chemistry, COMSATS University Islamabad, Lahore Campus, Lahore, 54000, Pakistan

    Lubna Sherin & Farah Kausar

Authors
  1. Yu-Ming Chu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Muhammad Kamran Siddiqui
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sana Javed
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Lubna Sherin
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Farah Kausar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Muhammad Kamran Siddiqui.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chu, YM., Siddiqui, M.K., Javed, S. et al. On Zagreb Type Molecular Descriptors of Ceria Oxide and Their Applications . J Clust Sci 33, 537–546 (2022). https://doi.org/10.1007/s10876-021-01984-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10876-021-01984-y

Keywords

Mathematics Subject Classification

Search

Navigation