A theoretical study of imogolite-like single wall nanotubes as a function of silicon and germanium content and their tubular radius is presented along with mapping of silicon-germanium content properties in models that contain from 9 gibbsite-like units $(N_u=9)$ to 13 gibbsite-like units $(N_u=13)$ with a silicon-germanium content $[X=\mathrm{Si}∕(\mathrm{Si}+\mathrm{Ge}\left)\right]$ of 0, 0.20, 0.40, 0.60, 0.80, and 1.00. The imogolite nanotubes were built setting periodic boundary conditions to density functional theory (DFT) geometry-optimized models along both radial and axial directions in order to obtain the stable structure. The DFT calculations were carried out on the $\Gamma$ point and for various $k$ points, using the GGA-PW91 functional, finding an optimal unit cell length of 8.72 and $8.62\mathrm{\AA }$ using a double numeric (DN) and double numeric with polarization (DNP) basis set, respectively, along the axial direction. The structural properties were analyzed through the evolution of the x-ray diffraction pattern as a function of both $N_u$ and $X$. A linear correlation between the tube radius and the position of the first two peaks on the x-ray diffraction is found. The imogolite surface charge was mapped with the Hirshfeld charge showing the characteristic acid tendency experimentally reported. The reactivity of imogolite-like structures was studied employing the total density of states and the band gap evolution as a function of $N_u$ and $X$ showing an increasing behavior with $X$. The local reactivity was analyzed by looking at the local density of states in models with $X=0.0$ and 1.0 with $N_u=10$. Finally, the frequency analysis was carried out in the optimized structure on the $\Gamma$ point finding a good agreement in the $\mathrm{O}\text{−}\mathrm{H}$ vibrations with those reported in the literature.

• Received 2 May 2007

DOI:https://doi.org/10.1103/PhysRevB.76.125421