Anomalous pressure behavior of tangential modes in single-wall carbon nanotubes

Using molecular-dynamics simulations and the force-constant model, we have studied the Raman-active tangential modes (TMs) of a (10,0) single-wall carbon nanotube under hydrostatic pressure. With increasing pressure, the atomic motions in the three TMs present obvious diversities. The pressure derivative of $E_{1g}$, $A_{1g}$, and $E_{2g}$ mode frequencies shows an increased value $(d{\omega }_{E_{1g}}∕dP>0)$, a constant value $(d{\omega }_{A_{1g}}∕dP\sim 0)$, and a negative value $(d{\omega }_{E_{2g}}∕dP<0)$ above $5.3\mathrm{GPa}$, respectively. The intrinsic characteristics of TMs consumedly help us understand the essence of the experimental $T$ band of CNT. The anomalous pressure behavior of the TM frequencies may originate from the tube symmetry alteration from $D_{10h}$ to $D_{2h}$ then to $C_{2h}$.

Figure 1

(Color online) (a) The cross-section shape elevation of (10,0) SWNT at some selected pressures (5.3, 5.5, 5.8, 6.1, and $6.8\mathrm{GPa}$, respectively), and corresponding symmetry group is attached. [(b)–(d)] The atomic motions of $E_{1g}$, $A_{1g}$, and $E_{2g}$ modes at symmetry transition pressures of 5.3, 5.5, and $6.1\mathrm{GPa}$, respectively.

Figure 2

The calculated amplitudes of half a unit cell atoms arranged in a line for (10,0) SWNT at some selected pressure (5.3, 5.5, 5.8, 6.1, and $6.8\mathrm{GPa}$ from top to bottom panels, respectively).

Figure 3

(Color online) (a) The energy as well as the length of the long and short axes as a function of pressure for (10,0) SWNT. [(b)–(d)] The calculated frequencies vs pressure of $E_{2g}$, $E_{1g}$, and $A_{1g}$ mode, respectively, and the pressure derivatives mentioned alongside.