Physical Analysis of Heat for Formation and Entropy of Ceria Oxide Using Topological Indices

Abstract

Background: Cerium oxide nanoparticles (C_eO₂ NPs) have gained their importance as engineered nanomaterials (ENMs) that have wide applications as catalysts in industry, which direct to their prominent occurrence in natural and engineered water systems. Cerium oxide nanoparticles (C_eO₂ NPs) have gained their importance as engineered nanomaterials (ENMs) that have wide applications as catalysts in industry, which direct to their prominent occurrence in natural and engineered water systems. In wastewater treatment plants, C_eO₂ 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 C_eO₂ NPs.

Aim and objective: The study was aimed to analyze the chemical graph of the crystal structure of Ceria Oxide(cuprite) C_eO₂. Also, our main objective is to compute the Heat of Formation and Entropy using degree based topological indices.

Materials and methods: 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. For calculation, we have utilized the combinatorial processing strategy, edge partition technique, vertex partition strategy, analytic procedures, graph hypothetical tools, degree counting technique and entirety of degrees of neighbor technique. Moreover, Matlab programming has been utilized for numerical computations and checks. We likewise utilized the maple for plotting these numerical outcomes.

Results: We have computed Heat of Formation and Entropy using degree based topological indices. Our main results are based on some degree based topological indices, namely, the atom bond connectivity index ABC, geometric arithmetic index GA, general Randi index, Forgotten index, Augmented zagreb index and Balban index for the chemical graph of the crystal structure of cuprite C_eO₂[p, q, t] We also provide a detailed application of the computed results.

Conclusion: We discuss these indices exhibited difference with the reported heat of formation and entropy of cuprite C_eO₂[p, q, t] In almost all the cases, an exponential increase of aforementioned indices is observed with the increase in the number of cells or other words size of cuprite C_eO₂[p, q, t] nanocrystal. On the other hand, a linear relationship of indices with respect to the number of formula units suggests a slight modification of these indices for an appropriate explanation of the physical properties of cuprite C_eO₂[p, q, t] nanocrystal of varying size and hence its prospective application in nanoceria engineering.

Keywords: Topological indices; ceria oxide; crystals.; cuprite; entropy; heat of formation.