Angular dependence of surfactant-mediated forces between carbon nanotubes

We employ dissipative particle dynamics to examine surfactant-mediated forces between two carbon nanotubes. Calculations are performed varying both the distance and the angle between the nanotubes. For small distances, a repulsive region is observed, followed by an overall attractive interval with strong oscillations in the force. Decreasing the angle between the tubes leads to a steady increase in the force, but the relative dependence on the separation distance is preserved. We find that the force scales linearly with the size of the overlap area between the tubes. This allows us to express the angle dependence by a simple equation, whereas the distance dependence is represented by a master curve. For the parallel case, the behavior is significantly different.