Column buckling of multiwalled carbon nanotubes with interlayer radial displacements

An elastic model is presented for column buckling of a multiwalled carbon n anotube embedded within an elastic medium. The emphasis is placed on the ro le of interlayer radial displacements between adjacent nanotubes. In contra st to an existing model which treats the entire multiwalled nanotube as a s ingle column, the present model treats each of the nested tubes as an indiv idual column interacting with adjacent nanotubes through the intertube van der Waals forces. Based on this model, a condition is derived in terms of t he parameters describing the van der Waals interaction, under which the eff ect of the noncoincidence of all deflected column axes is so small that it does not virtually affect the critical axial strain. In particular, this co ndition is met for carbon multiwalled nanotubes provided that the half-wave length of the buckling mode is much larger than the outermost diameter. In this case, the critical axial strain can be predicted correctly by the exis ting single-column model. On the other hand, the existing model could overe stimate the critical axial strain when the half-wavelength of the buckling mode is close to or smaller than the outermost radius.