Dynamics and Friction in Double Walled Carbon Nanotubes

The objective of this PhD thesis was the study of friction in carbon nanotubes by analytical methods and molecular dynamics simulations. The goal of this research was to characterize the properties of friction in nanotubes and from a more general point of view the understanding of the microscopic origin of friction. Indeed, the relative simplicity of the system allows us to interpret more easily the physical phenomenon observed than in larger systems. In order to achieve this goal, non-equilibrium statistical mechanics permitted first to develop models based on Langevin equations describing the dynamics of rotation and translation in double walled nanotubes. The molecular dynamics simulations then permitted to validate these analytical models, and thus to study general properties of friction such as the dependence on area of contact, temperature and the geometry of the nanotubes. The results obtained shows that the friction increases linearly with the sliding velocity or the angular velocity until very high values beyond that non-linearities appear enhancing dissipation. In the linear regime, it is shown that the proportionality factor between the dynamic friction force and the velocity is given by the time integral of the autocorrelation function of the restoring force for the sliding friction and of the torque for the rotational friction. Furthermore, a novel resonant friction phenomenon increasing significantly dissipation was observed for the sliding motion in certain types of nanotubes. The effect arises at sliding velocities corresponding to certain vibrational modes of the nanotubes. When the dynamics is described by the linear friction in velocity, the empirical law stating that friction is proportional to the area of contact is very well verified thanks to the molecular dynamics simulations. On the other hand, friction increases with temperature. VI Abstract The fact that friction increases as well with the area of contact as the temperature can be easily interpreted. Indeed, if the temperature is large enough so that the electronic effects can be negligible, dissipation is only due to the phonons. Indeed, it is the phonons who give the sliding or rotation energy to the other degrees of freedom until thermodynamic equilibrium is achieved. Thus, if the temperature increases, the coupling between the phonons and the rotational or translational motions increases, as well as friction. In the same manner, when the area of contact increases, the number of available phonons to transport energy increases, explaining thus the increase of the friction force.