Influence of Shape, Size, and Surface Effects on the Melting Temperature of Rutile (TiO₂) Nanoparticles: A Cohesive Energy Model Approach

The thermodynamic properties of nanoparticles, particularly their melting temperature, are strongly influenced by size, shape, and surface effects. In this study, we investigate the melting behavior of rutile-phase titanium dioxide (TiO₂) nanoparticles using a modified cohesive energy model that incorporates crystal structure and surface contributions. The model is applied to various nanoparticle shapes, including spherical, nanowire, nanofilm, octahedral, and hexahedral geometries, to assess their impact on melting temperature. Our results demonstrate a significant size-dependent reduction in melting temperature for nanoparticles in the 2–12 nm range, consistent with prior theoretical and molecular dynamics (MD) simulation studies. The cohesive energy model is refined to account for surface atom contributions, shape factors, and atomic packing efficiency, providing a robust framework for predicting melting behavior. Comparisons with existing MD simulations and Buffat-Borel model predictions reveal close agreement for larger nanoparticles (>6 nm), while slight deviations occur for smaller nanoparticles (<6 nm), likely due to enhanced edge and corner effects. Notably, the melting temperature decreases more rapidly for nanoparticles with higher shape factors, such as hexahedral and octahedral structures, compared to spherical nanoparticles of equivalent volume. In the absence of extensive experimental data, our theoretical predictions offer valuable insights into the thermodynamic stability of TiO₂ nanoparticles, which are crucial for applications in photocatalysis, photovoltaics, and nanotechnology. The findings highlight the importance of shape and size control in tailoring the thermal properties of nanomaterials for specific technological applications.