Deflection and pull-in instability of nanoscale beams in liquid electrolytes

An elastic beam suspended horizontally over a substrate in liquid electrolyte was subjected to electric, osmotic, and van der Waals forces. The problem, which is governed by four non-dimensional parameters, was solved using the finite element method. The sum of the electric and osmotic forces, the electrochemical force, is usually attractive. However, the electrochemical force can be repulsive for a narrow range of the ion concentration, the initial separation and surface potentials. Furthermore, the beam deflection is not a monotonic function of the applied surface potentials, the bulk ion concentration, or the initial separation between the beam and the substrate. As these parameters are increased monotonically, the beam bends up and then down. The pull-in voltage increases as the bulk ion concentration increases. The pull-in voltage of a double-wall carbon nanotube suspended over a graphite substrate in liquid can be less than or greater than the pull-in voltage in air, depending on the bulk ion concentration. The critical separation between the DWCNT and the substrate increases with the bulk ion concentration. However, for a given bulk ion concentration, the critical separation is independent of the electric potentials. Furthermore, the critical separation is approximately equal in liquid and air.