An approach to the experimental determination of the bending stiffness of nanosize shells

Abstract

The problem of the experimental determination of elastic moduli of nanoscale objects is of present interest. The determination of the elastic moduli of thin macroscopic shells is usually based on experiments with plates. It is known that, when grown using certain techniques, nanoobjects are obtained only in the form of shells. Therefore, it is necessary to develop a method for determining the elastic moduli of nanoobjects on the basis of experiments with shells. Experimental determination of the bending stiffness of nanosize shells presents a serious problem, because for such widespread nanoobjects as nanotubes and fullerenes under arbitrary deformation, the material is subjected to both bending and tension. Therefore, all parameters (e.g., natural frequencies) that can be measured directly are complicated functions of both bending and tension stiffness. In recent years, together with nanotubes and fullerenes, nanoobjects of a more intricate configuration have been obtained [1‐4]. Nanosize cylindrical helices [1, 3] are of particular interest in connection with the possible experimental determination of bending stiffness. This is due to the fact that (1) in helical shells under arbitrary deformation, the material is mainly bent, so that the material tension effect can be neglected when interpreting experimental data; and (2) the natural oscillation shapes of helical shells are much more easily observed than those of cylindrical shells associated with pure bending of the material. The latter statement is illustrated in Fig. 1, which presents the first four helical shell oscillation shapes. The analysis of helical shell dynamics [5] presented below may be a theoretical foundation for experimental testing of the applicability of the continuum theory to (a) the calculation of mechanical characteristics of nanoobjects and (b) the experimental determination of the bending stiffness of nanoshells.