Strain energy minimum and vibrational properties of single-walled aluminosilicate nanotubes

We study the origin of the strain energy minimum in a single-walled aluminosilicate nanotube via a harmonic force-constant model and molecular dynamics simulations. The model is based on a circular cross-section geometry of the nanotube composed of semirigid $\mathrm{Al}{\mathrm{O}}_6$ octahedra and $\mathrm{Si}{\mathrm{O}}_4$ tetrahedra. The monodispersity in the nanotube diameter is explained in terms of a minimum in the strain energy due to differences in bond energies on the inner and outer surfaces. The model also reproduces the diameter dependence of the radial breathing mode (RBM) frequency and is in accord with midinfrared spectroscopic characterization.

Figure 1

(Color online) (a) Building unit of aluminosilicate nanotube showing hexagonal arrangement of aluminum atoms, bridging oxygens, and pendant silanol. (b) Perspective view of the unit cell of a nanotube with 24 aluminum atoms in the circumference. Green (dark gray); Al, Gold (light gray); Si, Red (black); O, Gray: H.

Figure 2

(a) Total energy per atom at $298\mathrm{K}$ of the nanotube vs the number of aluminum atoms in the circumference. (Inset) Nanotube radius and distance $d_{\mathrm{Al}\text{−}\mathrm{Al}}$ vs the number of aluminums in the circumference. (b) Radial breathing mode frequency vs nanotube radius. Symbols denote results of atomistic calculations and solid lines are model fits.

Figure 3

Bond strain energies [Eq. (1)] of Al-O and Si-O vs the number of aluminum atoms in the circumference.