Superfluidity inside carbon nanotubes

Molecular dynamics simulations of equilibrium structures and flows of nonpolar argon atoms confined by single-walled carbon nanotubes (SWCNTs) with circular cross section and rectangular cross section having the same area and the ratio between its sides $1:4$ have been performed. It has been shown that, inside these SWCNTs, argon atoms form the spatially ordered structures and, under action of external driving forces they move collectively along SWCNT's axes. It has been also obtained that there are two regimes of such collective movement. In the first regime, when the driving external force $f_{x0}$ is lower than a certain critical value $f_{xc}$, argon atoms flow through these SWCNTs with the finite average flow velocity. In the second regime, when the driving external force $f_{x0}$ exceeds $f_{xc}$, the retarding friction force acting on argon atoms from bounding wall carbon atoms gradually drops to zero and the average flow velocity exhibits an unlimited growth. Moreover, when the retarding friction force becomes close to zero, the fluid will continue to flow with the same constant velocity at switched off external driving force. Hence, in the second regime, argon atoms inside the above-mentioned SWCNTs demonstrate the ballistic frictionless flows which resemble the superfluidic liquid flow. It has been shown that collective frictionless ballistic flows of argon atoms through SWCNTs are caused by the crystalline structure of SWCNT's bounding walls and, for the same SWCNTs with random distribution of carbon atoms on the bounding walls, one can observe only the first regime of the argon atom flows.

Figure 1

The lateral projections (the tube axes are parallel to the $x$ axis) and cross sections of SWCNTs used in our MD simulations. (a) SWCNT with rectangular cross section and with the ratio between its sides $1:4$; (b) SWCNT with circular cross section.

Figure 2

The lateral projection of initial and final equilibrium configurations considered in our MD simulations. (a) initial configuration; (b) final equilibrium configuration. Blue circles are argon atoms and red ones are carbon atoms.

Figure 3

The lateral projection (a) and cross section (b) of equilibrium structure of argon atoms inside SWCNT with rectangular cross section depicted in Fig. 1. Red circles denote the bounding wall carbon atoms and blue circles denote argon atoms. (c) is the corresponding density profile along $y$ axis perpendicular the lateral bounding walls.

Figure 4

The cross section of equilibrium structure formed by argon atoms inside SWCNT with circular cross section (a). (b) The corresponding radial density profile.

Figure 5

Time dependencies of average argon flow velocities $v_x$ through SWCNTs with circular and rectangular cross sections. Curve 1: the first regime ($f_{x0}=0.09$) for SWCNT with circular cross section; curve 2: the second regime ($f_{x0}=0.1$) for the same SWCNT; curve 3: after switching off the external driving force ($f_{x0}=0$), circular cross section; curve 4: the argon atom flow through SWCNT with rectangular cross section and bounding wall consisting of carbon atoms randomly distributed on its surface, $f_{x0}=0.2$; curve 5: $T=1.24K, f_{x0}=0.09$.

Figure 6

Typical time dependence of instantaneous retarding force $f_{Rx}$ acting on argon atoms from bounding wall carbon atoms during argon flow through SWCNT with circular cross section

Figure 7

Time dependencies of the ratio $|f_{Rx}|/f_{x0}$ averaged over consecutive time intervals during the argon atom flows through SWCNTs with circular and rectangular cross sections. Curve 1: the first regime ($f_{x0}=0.09$), circular cross section; curve 2: the second regime ($f_{x0}=0.1$), circular cross section; curve 3: the argon atom flow through SWCNT with rectangular cross section and bounding wall consisting of carbon atoms randomly distributed on its surface, $f_{x0}=0.2$; curve 4: $T=1.24K, f_{x0}=0.09$.