Pressure-induced hard-to-soft transition of a single carbon nanotube

We demonstrate a hydrostatic pressure-induced hard-to-soft transition of an isolated single wall carbon nanotube, using classical and ab initio constant-pressure molecular-dynamics simulations and continuum elastic theory analysis. At low pressure, the carbon tube is hard. Above a critical pressure, the tube becomes much softer with a decrease of bulk modulus by two orders of magnitude. The hard-to-soft transition is caused by a pressure-induced shape transition of the tube cross section from circular to elliptical.

Figure 1

The energy and pressure as a function of the reduced volume for (10,10) nanotube at $300\mathrm{K}$. The energies are relative to the minimum energy, and the volume is normalized by the equilibrium volume without the external pressure. At about $1.0\mathrm{GPa}$, the hard phase with bulk modulus of about $100\mathrm{GPa}$ transforms into the soft phase with bulk modulus of just a few GPa.

Figure 2

(a) The length of the long and short axes, as a function of pressure for (10,10) nanotube. The shape of the cross section at some selected pressures is plotted at the bottom of the figure. (b) The absolute relative change of bond length and bond angle as a function of pressure for (10,10) nanotube, the data is obtained by quenching the system from 300 to $0\mathrm{K}$ at constant pressure.

Figure 3

The transition pressure (upper panel) and the elastic modulus (lower panel) as a function of tube radius at $300\mathrm{K}$. The solid line is a least-squares fit to the data using Eq. (4) (upper panel) and Eq. (6) (lower panel). The simulated data follows nicely with the predicted behavior.

Figure 4

The energy and pressure as a function of the reduced volume for (6,6) nanotube at $300\mathrm{K}$, obtained by ab initio molecular dynamics. The energies are relative to the minimum energy, and the volume is normalized by the equilibrium volume without the external pressure. The hard to soft transition can be observed at about $10.5\mathrm{GP}$.