content_image/342277.jpg content_image/342278.jpg content_image/342279.jpg content_image/342280.jpg content_image/342282.jpg
## EQUATION OF MOTION 

## Supplementary Information Thermophoretically Driven Carbon Nanotube Oscillators 

V. R. Coluci, V. S. Tim´ oteo, and D. S. Galv˜ ao 

The motion of the inner tube of the CNT oscillator considering only translational motions (rigid tubes) is given by 

where the restoring force is written as 

<img src='content_image/342277.jpg'>

<img src='content_image/342278.jpg'>

with 

( δ = 0 . 1 ˚ A) and 

<img src='content_image/342279.jpg'>

<img src='content_image/342280.jpg'>

where F$_{vdW}$ is the magnitude of the van der Waals restoring force, L and l are the outer and inner tube lengths, respectively. The form of F ( x ) is shown in Fig. S1, for L = 100 nm and l = 5 nm. 

The thermal gradient was chosen to be practically constant on the outer tube length based on molecular dynamics simulations (see below) according to the following expression 

<img src='content_image/342282.jpg'>

Thus, the term αdT/dx represents the thermal force due to thermal vibrations of the outer tube caused by the externally imposed thermal gradient (Fig. S1). The regime of a constant thermal gradient is obtained after a transient period once the electrical current pulse is applied. We have analyzed the dynamics of the transient period using molecular dynamics simulations (see below). 

