Simple expressions of the nuclear relaxation rate enhancement due to quadrupole nuclei in slowly tumbling molecules

The aluminosilicate mineral imogolite is composed of single-walled nanotubes with stoichiometry of (HO)(3)Al(2)O(3)SiOH and occurs naturally in soils of volcanic origin. In the present work we study the stability and the electronic and mechanical properties of zigzag and armchair imogolite nanotubes using the density-functional tight-binding method. The (12,0) imogolite tube has the highest stability of all tubes studied here. Uniquely for nanotubes, imogolite has a minimum in the strain energy for the optimum structure. This is in agreement with experimental data, as shown by comparison with the simulated X-ray diffraction spectrum. An analysis of the electronic densities of states shows that all imogolite tubes, independent on their chirality and size, are insulators.