Analysis of quantum effects of fine scaling on the axial buckling of MWCNTs based on the density functional theory and molecular mechanics method

In this paper, quantum and molecular mechanics are used to study the quantum effects of fine scaling on the buckling strength of multi-walled carbon nanotubes under axial loading, as well as the effects of changes in length, diameter, chirality, wall number and length-to-diameter ratio of the structure. To this end, the total potential energy of the system is calculated with the consideration of both bond stretching and bond angular variations. The density functional theory along with the generalized gradient approximation function is used to obtain the relevant elastic constants of the nanotubes. An excellent agreement is found between the present numerical results and those found in the literature which confirms the validity as well as the accuracy of the present closed-form solution. The results show that in the effective longitudinal range for quantum effects of fine scaling, any change that leads to a change in the size of the structure has significant effects on the buckling strength of the structure. By increasing the diameter due to the increase in the number of walls or chirality and increasing the length of the structure, the critical buckling strength experiences a decreasing trend and this decrease is highly dependent on the increasing of the diameter due to the increase in the number of walls. In addition, zigzag multi-walled carbon nanotubes are more resistant than armchair multi-walled nanotubes, and the critical buckling strain of multi-walled carbon nanotubes with different chiralities is in the range of zigzag and armchair nanotubes. In other words, it can be said that quantum effects of fine scaling cause more buckling strengthening of the structure against external axial loads and with each longitudinal change that reduces the quantum effects of fine scaling, the strength of the structure decreases sharply.