Size-Dependent Variation of Relaxation Factor in Nanomaterials: A Theoretical and Comparative Study

Abstract

The study investigates the relaxation factor (τ) for different sized and shaped ZnO, TiO₂, Al2O₃, Fe2O₃, and CuO nanostructures. Surface scattering, lattice strain, and quantum confinement were all included in the theoretical framework. The spherical, octahedral, tetrahedral, and cylindrical and hexagonal nanowires as well as thin films were all calculated. Strong surface scattering is indicated by the data's quick τ increase for D < 5 nm, and saturation near bulk behaviour is seen beyond D = 10 nm. Tetrahedral nanoparticles revealed the lowest τ values because of their better confinement, whereas thin films consistently showed larger values. The reliability of the model is confirmed by comparison with published literature. These results enable future studies in heat transport applications based on nanomaterials and offer insights for thermal control in nanoscale devices (Balandin, 2005; Zou & Balandin, 2001; Feng et al., 2015).