Low-dimensional phonon specific heat of titanium dioxide nanotubes

The specific heat of multiwalled titanium dioxide (anatase phase) nanotubes has been measured between 1.5 and 95K. Bulk anatase and rutile were also measured. The nanotube specific heat approaches that of bulk anatase at high temperatures. Below about 50K the nanotube specific heat begins to show large enhancements compared to bulk. Using an isotropic elastic continuum model, this can be understood qualitatively as a transition to low-dimensional behavior. Below about 3K there is a second transition and the nanotube specific heat becomes nearly constant, exceeding bulk anatase by an order of magnitude or more at 1.5K.