Physical Mechanics And Analytical Model Of Thermophoresis In Carbon Nanotubes

Nanoactuators are nanoscale devices that convert energies into motions. Because of their broadly potential applications ranging from artificial muscles to data storage, nanoactuators have attracted considerable interest in scientific community. Carbon nanotubes are marvelous nanostructures. Since discovered by Iijima, they have been ideal building blocks in nanoscale devices due to their extraordinary electrical, mechanical, chemical, and thermal properties (such as their low density, high stiffness and strength, chemical inert, electronic properties from metallic to semiconducting). In addition, their one dimensional tubular shape and multi-shell structure have been the key components for the fabrication of nanotube-based devices. The tubular shape restricts the relative motions to only rotation and translation. The multi-shell structure makes the carbon nanotubes a natural movable device. In the last decade, large numbers of nanotube-based nanoactuators have been designed.We consider a system that consists of a short outer nanotube and a long inner nanotube. A temperature gradient exists along the inner tube. The outer tube are driven to the cold zone by a force generated by the thermal gradient. Via molecular dynamics simulations, we found that the thermophoretic force is composed of two parts. The first part, called gradient force (which is caused by a gradually distributed vdW potential along the inner tube), is exerted on all atoms of the outer tube; while the second, called the unbalance pinch force (induced by the difference of edge forces which are resulted from edge barrier near the outer tube), is exerted only on the edge atoms of the outer tube. A complete understanding for the origin of thermophoretic force needs an analysis of the temperature dependent vdW potential energy between coaxial nanotubes. We define the reference potential as the vdW potential of a system in which all atoms are in their equilibrium positions. When atoms are away from their equilibrium positions, the system potential increases. This thermal induced increase in vdW potential is called additional vdW potential. The system potential is obviously dependent on temperature. The gradient force exerted on an atom of the outer tube can be obtained by differentiating the vdW potential energy between the atom and the inner tube with respect to the axial position of the atom. The pinch force can be derived as same way. Thus an analytic model is proposed and a closed form solution for the thermophoretic force is obtained.