Geometrical confinement effects on fundamental thermal properties of rutile and anatase TiO2 cylindrical and tubular nanostructures

Abstract

Abstract In this work, we investigated the influence of the geometrical confinement effects on the fundamental thermal properties of rutile and anatase TiO2 for both cylindrical nanostructures (CNSs) and nanotubular structures (NTSs), respectively. Calculations of energy levels are developed in the framework of effective mass approximation by generalizing the resolution of Schrödinger equation in a truncated cylinder. The energy spectrum is then used in the determination of thermodynamic properties by using the Boltzmann-Gibbs distribution. Numerical computations done for both rutile and anatase TiO2 nanomaterials reveal a strong localization of the electron orbitals along to the lateral surface for all the studied are CNS and NTS. The average energy, heat capacity, entropy, and Helmholtz free energy calculated for different thicknesses for NTS and different cross-sections of CNS. Our numerical investigation shows that all thermodynamic properties depend on the temperature, the cross-section for the CNS, and the shell thickness for the NTS. We demonstrated that for low thickness, the heat capacity shows a Schottky-like anomaly at low temperatures. We also show that the Rutile structure is more stable than anatase. We hope that the thermodynamic properties concluded from this study can be considered as useful information for understanding the thermodynamic properties of TiO2 nanofibers.