Kinetic Investigation On Interactions Of Fast Ions With Carbon Nanotubes

Theoretical study has been put forward on interactions of fast ions with carbon nanotubes in this paper. A semi-classical kinetic model is developed to simulate the electron excitation of surface gas of nanotubes, the dynamical polarization force for zigzag and armchair nanotubes, respectively, and the trajectory of charged particles through zigzag nanotubes. With the introduction of electron band structure, the analytical expressions of the dielectric function and the energy loss function are obtained for zigzag and armchair nanotubes. And the induced electron density, induced potential, self-energy and stopping power are calculated with the intrusion of ions. Besides, the atomic dynamic repulsion is described by a continuum potential based on the Thomas-Fermi-Moliere model. By solving Newton's equations for ion motion, we can get the ion trajectory through zigzag showing the ion velocity and position.It is found from the calculations that: the dielectric function and energy loss function of nanotubes are not only interrelated with the friction coefficientγ, the wave number k, the angular momentum m but also with the radius and chiral angle of zigzag and armchair nanotubes. Considering a proton moving along the axis of nanotubes, the calculation results of induced electron density and induced potential show that there exists a proton threshold speed, below which the induced electron density on the nanotube surface takes on a bell-like distribution, while for the speeds above the threshold, the induced electron density has a wake-like oscillation distribution. And we found that the induced electron density presents two different kinds of trends for low and high proton velocity. From the calculation of the self-energy and the stopping power, we could easily observe that both of the self-energy and the stopping power keep decreasing in magnitude, when the value ofγincreases. Moreover, the self-energy negative peaks and the stopping power maxima move to lower velocities with the increasing of friction coefficientγvalues. It means that the plasmon resonance broadens with great friction force between the positive charge and the valence electrons of nanotube surface atoms. Provided the ion initial position is not too close to the nanotubes wall, the incident angle is sufficient small, it is found that, trajectories oscillate over peripheral radial regions in the zigzag nanotube, owing to the dynamical polarization of the surface gas of nanotube.