The size dependence of the surface free energy of titania nanocrystals

We determined the lattice contraction of nanocrystalline anatase (TiO ₂) as a function of particle size (∼4-34 nm) using X-ray diffraction and Rietveld analysis. Surface free energy (γ) of nanocrystalline anatase was derived from these data from an integration of the surface stress calculated from the lattice contraction. Our results revealed an unexpected strong size dependence of γ with a maximum value at around 14 nm. Two opposing factors contribute to the variation of γ with the particle size, the increase of surface free energy with decreasing particle size due to presence of more high-energy sites, and the decrease of surface free energy due to closer structural correspondence between surfaces and interiors of nanoparticles as the particle size decreases. Our approach may be used to study nanoparticles in cells and other environments where conventional calorimetric measurements of nanoparticle surface enthalpy are not applicable.