Theory of simultaneous control of orientation and translational motion of nanorods using positive dielectrophoretic forces
The manipulation of individual submicron-sized objects has been the focus of significant efforts over the last few years. A method to arbitrarily move and orient a set of rod-shaped conductive particles in a region defined by a set of electrodes using positive dielectrophoretic forces is presented. While the orientation of each particle is directly specified through the angle of the local electric field, its position is indirectly controlled through the applied force. Each electrode is approximated as an unknown point charge and an induced dipole. Since each induced dipole results from the combination of all other sources, a set of linear constraints are derived to enforce the self-consistency of the system. Additionally, the force and orientation of each particle also form an additional set of linear constraints. This combined set of constraints is then solved numerically to yield the sources required to induce the desired orientation and motion of each particle. It is observed that the minimum number of electrodes that can be used to control a set of N particles is 4N+1. Numerical simulations demonstrate that the control of a single nanorod (diameter of 70 nm; length of 1.4μm) in the midst of a realistic electrode array can be accomplished under practical conditions. In addition, such control of orientation and motion can be achieved over an ample region in the vicinity of each rod.