Manybody effects at low-energy ions channeling in carbon nanotubes

The molecular dynamics method has been used to consider manybody interactions at the channeling of the ion in a carbon nanotube, and the importance of their accounting has been shown. The effect of the wall elastic perturbation of a nanotube on a channeled particle is studied. It was confirmed that when ion with perturbation of the wall of the carbon nanotube interaction is taken into account, the ion energy loss is reduced by a factor of 1.5-3. It is shown that as the temperature of the nanotube decreases, the effect of ion interaction with wall perturbation acquires a more determinate character. Within the framework of the considered model, electronic stopping power on the electronic subsystem of a carbon nanotube is small compared to energy losses of an ion in elastic collisions on atoms of a nanotube wall.


Introduction
After the discovery of carbon nanotubes (CNTs) and the discovery of their unique properties, they found application in many areas of solid state physics. Interesting applications are 1) the use of carbon nanotubes as channels for ion transport [1-3]; 2) creation of nanocontainers from carbon nanotubes by means of ion implantation [4,5]. On the one hand, both applications are applicable to chemistry and biology for the delivery of substances to the cell, to the chemical reaction zone. On the other hand, the first application is applicable for precise control of an ion beam during ionic modification of a solid surface [6,7], and the second can be useful in the modification of the chemical and electronic properties of the nanotubes themselves. The ion modification of carbon nanotubes was studied in works of Nordlund [8][9][10][11][12][13], Shemukhin [14-16] both theoretically and experimentally. Transport of ions through the channels of nanotubes was studied mainly theoretically by computer simulation [17]. The author knows only one experimental work [18] on the transport of ions through an array of multiwalled carbon nanotubes grown in the pores of porous alumina. Theoretically, channeling of ions in carbon nanotubes was studied for three energy ranges: high (~1GeV) [19][20][21], medium (~1 MeV) [22][23][24][25][26][27][28][29][30] and low (~1 keV) [31][32][33][34][35]. When channeling the ion, it interacts with the atoms of the wall of the carbon nanotube, collisions of ions and CNT wall atoms usually occur at sliding incident angles. Depending on the energy of the ion, it is possible to exhibit both elastic and inelastic scattering of the ion on CNT wall atoms. It should be noted that in the low-energy range, ion energy losses predominate over elastic collisions of an ion with CNT wall atoms. In the middle energy range, the energy losses associated with the stopping of CNT walls on an electron gas are more pronounced. In the high-energy range, there is a collective interaction of the ion with atoms and inelastic scattering by electrons of the nanotube wall. 2 Historically, the high energy range was first investigated. To control beams of high-energy ions as an alternative to cumbersome magnetic systems, it [36] has been proposed to use nanotubes. In the works [21,37] was shown that the fluxes of ions of high (ultra relativistic) energies can be controlled by CNT bundles or multiwalled CNTs better than curved crystals. Beams of medium-energy ions interact predominantly with the electron subsystem of the nanotube, which affects the nature of channeling in nanotubes and energy losses [26,38,39]. In the low-energy range, nuclear (elastic) inhibition predominates, and the interaction of ions with the atoms of the tube is due to manybody interactions [17,31,39]. Manybody collisions are collisions influenced by the position, type, and degree of hybridization of neighboring atoms. The channeled ions in this energy range are rapidly neutralized [31]. Earlier it was shown that it is important to take into account the motion of all atoms in the nanotube, and not only the nearest ion to the channeled one. Using the method of molecular dynamics, results were obtained on the passage of ions through carbon nanotubes with heterojunctions [40], which can be used as focusing apertures for low-energy particles.
In this paper, we demonstrate the effects observed when many-body interactions are taken into account in modeling the channeling of low-energy ions in carbon nanotubes.

Methods
For the calculations in this paper we used the molecular dynamics method. The LAMMPS code was used [41]. Carbon nanotubes were created using the VMD code [42], visualized using Ovito [43].
It is important to take into account the manybody interactions of the ion and the atoms of the nanotube. The use of the classical approach to describe such interactions is confirmed in [44], using the time-dependent density functional theory method.
For molecular dynamics calculations, carbon nanotubes were first prepared. The coordinates of the atoms were created using the VMD code, three models of nanotubes ["armchair" (10, 10), "zig-zag" (17, 0) and "chiral" (11, 9)] were constructed with approximately equal diameters (1.3 nm), the length of each of the tubes was 14.3 nm. To describe the interatomic interactions of carbon atoms the AIREBO potential was used [45]. Then, using the conjugate gradient method with the LAMMPS code, the energy of the carbon nanotube was minimized, and then the thermostat of Berendsen [46] for 5 ps and a relaxation time of 0.1 ps and Nose-Hoover [47] also for 5 ps and a relaxation time of 0.1 ps with an integration step of 1 fs.
To calculate the trajectories of channeled ions, the following initial conditions were applied: the ions were launched from the nanotube axis with incident energy 100 eV for all cases, the angle of incidence α varied from 10 to 30 °, the azimuth angle θ varied from -18 to +18º) and the initial position on the Z axis was chosen from 0 to 0.24 nm. As the interaction potential of the ion with the atoms of the nanotube's wall Ziegler-Biersack-Littmark (ZBL) potential was used [48]. In addition, the inelastic deceleration force on an electron gas was taken into account using the formula obtained in the framework of the classical electromagnetic theory in the works [31, 49]: -surface plasmon frequency,  -distance between ion and nanotube wall, Fermi velocity (here we use Hartree units, unless otherwise indicated). All parameters listed here concise with metallic carbon nanotubes ('arm-chair' chirality).
The step of integrating the equations of motion 0.0005 fs as a result of the trajectories obtained was analyzed: ion collisions with the nanotube wall were tracked, changes in the total ion energy after each collision were calculated. Dependences of ion energy losses in collisions versus the angle of entry α were obtained, with the results at each angle of entry being averaged over the azimuthal angles and the initial position on the Z axis. The total number of spans per tube was 13689, that is, for each angle of entry α, 169 span.

Results and Discussion
The trajectory of the ion inside the carbon nanotube is shown in figure 1. The general view of the trajectory is shown in figure 1 a sections of the trajectory of the ion and the state of the atoms of the tube when the atom approaches the wall is shown in figure 1 b. When the ion collides with the wall, the carbon atoms move from the equilibrium position and the wall deforms.  Figure 2 shows the dependence of the relative displacement of the atoms of the wall of the tube as a function of time during the first collision of an ion with the nanotube wall. As can be seen from figure 2 there is a simultaneous displacement of several wall atoms. This proves the validity and validity of a more consistent method of molecular dynamics, in contrast to the approximation of pair collisions or models based on averaging the potential of the nanotube wall that does not take into account the atomic displacements. It should be noted that this statement is most true at relatively large ion channeling angles. The displacement of atoms generates the appearance of a perturbation on the wall of the nanotube and affects neighboring carbon atoms, including diametrically opposite to those encountered by the ion. The perturbation propagates along the axis of the nanotube, and the propagation velocity of the perturbation is approximately 16 km/s, which is close to the propagation velocity of phonons in a carbon nanotube [50,51]. Simulation shows that the perturbation of the tube wall can propagate at a velocity close to the longitudinal velocity of ion motion, in this case the perturbation can interact with the ion. Earlier in the work [52] it was shown that the interaction of the ion with the perturbation caused by it leads to a decrease in the energy loss by the ion in a collision with the wall. If we compare the graphs of the dependence of the energy loss of an ion on the angle of entry, taking into account the perturbation of the nanotube wall and without taking into account  3), it turns out that for the second and third collisions in the model, taking into account the wall perturbation, the ion is lost by 1.5-3 times less energy than in model without taking into account the perturbation of the nanotube wall. This is explained by the exchange of energy between the perturbation of the wall and the moving ion -there is a gliding of the particle on the wave of perturbation of the nanotube wall [52]. Such a phenomenon becomes possible if the longitudinal velocity of the particle and the propagation velocity of the perturbation along the tube axis are close. This conclusion is also confirmed by the fact that when the longitudinal component of the ion velocity increases, the effect of energy exchange between the perturbation and the ion is not so significant. It was previously shown that for the Ar + ion the observation condition of the effect can be represented in the form of a range of angles (21-28 degrees) and energies (20 -55 eV) of the ion. We have obtained data on the effect of temperature on the character of the ion energy losses as a function of the initial angle of entry, with and without electronic stopping. The dependences indicate a non-monotonic character of the dependence of the ion energy losses on the angle of flight. It was shown that the inclusion of electronic inhibition does not make a significant contribution to the character of the dependences of energy loss by an ion on the angle of entry (figure 4). But taking into account the temperature of the nanotube affects on the energy loss vs incident angle dependencies. So nanotubes at low temperature are less subject to the influence of temperature fluctuations, and as a result, the curve of the dependence of ion energy loss as a function of the angle of entry looks more deterministic. Since nanotubes of various chiralities were investigated, but diameters for each of them were close, analogous dependences of ion energy losses on the angle of entry into the tube were constructed. For the second and third collisions with the wall, the form of the dependences (figure 5) differs somewhat especially for room temperature, but on average they are close, and the differences disappear at a temperature of 0.1 K (figure 6).   Figure 5. The loss of energy after the second (second to the left) and third (third to the right) collisions of the Ar + ion with the CNT wall (at a temperature of 300 K), depending on the initial channeling angle for the "armchair" (10, 10), "chiral" (11, 9) and "zig-zag" (17, 0) nanotubes. Figure 6. The loss of energy after the second (second to the left) and III (third to the right) collisions of the Ar + ion with the wall of the CNT (at a temperature of 0.1 K), depending on the initial channeling angle for the "armchair" (10, 10), "chiral" (11, 9) and "zig-zag" (17, 0) nanotubes.

Conclusion
When approaching the CNT wall, the channeled particles experience an effective interaction simultaneously with several atoms, and an elastic deformation of the wall takes place. Hence, the incomplete adequacy of the approximation of the continuous potential, the binary collision model, and the need to use the molecular dynamics method in modeling the channeling process follow.
An elastic perturbation of the nanotube wall under the action of a channeled particle affects the motion of this particle if its velocity is close to the propagation velocity of the perturbation. At the same time, the particle loses less energy than in the case of motion in the unperturbed tube.
The temperature oscillations of the atoms of a carbon nanotube randomize the trajectory of the channeled particle. With decreasing temperature, the dependence of the ion energy loss on the angle of entry upon collision with the wall acquires a more determinate character.