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Size- and chirality-dependent mechanical properties of single-walled zinc oxide nanotubes (ZnONTs) under four different states of hydrogen adsorption have been investigated in this paper. A molecular mechanics model is developed to derive analytical expressions for surface Young’s modulus and Poisson’s ratio of chiral hydrogenated ZnONTs (H-ZnONTs). On the basis of quantum mechanics, density functional theory (DFT) is utilized to obtain the force constants of molecular mechanics theory. Also, the values of surface Young’s modulus, bending stiffness, Poisson’s ratio, and atomic structure of a hydrogenated zinc oxide (H-ZnO) sheet associated with the four positions of adsorption are determined via the DFT calculations. The related results indicate that the bending stiffness of a H-ZnO sheet is chirality-independent. The present analysis provides the possibility of considering nanotubes with different types of chirality. It is indicated that, for all positions of hydrogen adsorption, the values of surface Young’s modulus for armchair H-ZnONTs are higher than those of zigzag H-ZnONTs and the results of chiral H-ZnONTs are between the results of armchair and zigzag nanotubes. Also, the maximum stability happens when the hydrogen atoms are adsorbed on zinc and oxygen atoms at the two opposite sides of a ZnO sheet.